Deck 8: Complex Numbers and Polar Coordinates

ملء الشاشة (f)
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سؤال
Combine the complex numbers. <strong>Combine the complex numbers.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>

A)​ <strong>Combine the complex numbers.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
B)​ <strong>Combine the complex numbers.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
C)​ <strong>Combine the complex numbers.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Combine the complex numbers.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Combine the complex numbers.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
استخدم زر المسافة أو
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لقلب البطاقة.
سؤال
Find the product. <strong>Find the product.   ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find the product.   ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the product.   ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the product.   ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the product.   ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the product.   ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the product. <strong>Find the product.   ​</strong> A)​   B)​   C)   D)   E)​   <div style=padding-top: 35px>

A)​ <strong>Find the product.   ​</strong> A)​   B)​   C)   D)   E)​   <div style=padding-top: 35px>
B)​ <strong>Find the product.   ​</strong> A)​   B)​   C)   D)   E)​   <div style=padding-top: 35px>
C) <strong>Find the product.   ​</strong> A)​   B)​   C)   D)   E)​   <div style=padding-top: 35px>
D) <strong>Find the product.   ​</strong> A)​   B)​   C)   D)   E)​   <div style=padding-top: 35px>
E)​ <strong>Find the product.   ​</strong> A)​   B)​   C)   D)   E)​   <div style=padding-top: 35px>
سؤال
Is <strong>Is    a solution to the equation   ? ​</strong> A)no B)yes <div style=padding-top: 35px>  a solution to the equation <strong>Is    a solution to the equation   ? ​</strong> A)no B)yes <div style=padding-top: 35px> ? ​

A)no
B)yes
سؤال
Let <strong>Let    and    and find   . ​</strong> A)   B)   C)​   D)​   E)​   <div style=padding-top: 35px>  and <strong>Let    and    and find   . ​</strong> A)   B)   C)​   D)​   E)​   <div style=padding-top: 35px>  and find <strong>Let    and    and find   . ​</strong> A)   B)   C)​   D)​   E)​   <div style=padding-top: 35px> . ​

A) <strong>Let    and    and find   . ​</strong> A)   B)   C)​   D)​   E)​   <div style=padding-top: 35px>
B) <strong>Let    and    and find   . ​</strong> A)   B)   C)​   D)​   E)​   <div style=padding-top: 35px>
C)​ <strong>Let    and    and find   . ​</strong> A)   B)   C)​   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Let    and    and find   . ​</strong> A)   B)   C)​   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Let    and    and find   . ​</strong> A)   B)   C)​   D)​   E)​   <div style=padding-top: 35px>
سؤال
Let <strong>Let    and    and find   . ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>  and <strong>Let    and    and find   . ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>  and find <strong>Let    and    and find   . ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> . ​

A) <strong>Let    and    and find   . ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Let    and    and find   . ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Let    and    and find   . ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Let    and    and find   . ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Let    and    and find   . ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Combine the complex numbers. <strong>Combine the complex numbers.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>

A) <strong>Combine the complex numbers.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
B)​ <strong>Combine the complex numbers.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
C)​ <strong>Combine the complex numbers.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Combine the complex numbers.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Combine the complex numbers.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
سؤال
Write the expression <strong>Write the expression    in terms of i.</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>  in terms of i.

A)​ <strong>Write the expression    in terms of i.</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
B)​ <strong>Write the expression    in terms of i.</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
C)​ <strong>Write the expression    in terms of i.</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Write the expression    in terms of i.</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Write the expression    in terms of i.</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
سؤال
Simplify the power of i . ​ <strong>Simplify the power of i . ​   ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Simplify the power of i . ​   ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Simplify the power of i . ​   ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Simplify the power of i . ​   ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Simplify the power of i . ​   ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Simplify the power of i . ​   ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find x and y (real numbers)so that the equation is true. <strong>Find x and y (real numbers)so that the equation is true.   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>

A)​ <strong>Find x and y (real numbers)so that the equation is true.   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>
B)​ <strong>Find x and y (real numbers)so that the equation is true.   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>
C)​ <strong>Find x and y (real numbers)so that the equation is true.   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>
D)​ <strong>Find x and y (real numbers)so that the equation is true.   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>
E) <strong>Find x and y (real numbers)so that the equation is true.   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>
سؤال
If z is a complex number then the product of z and its conjugate is a real number. ​

A)false
B)true
سؤال
Let Let    and    and find   .  <div style=padding-top: 35px>  and Let    and    and find   .  <div style=padding-top: 35px>  and find Let    and    and find   .  <div style=padding-top: 35px> . Let    and    and find   .  <div style=padding-top: 35px>
سؤال
Find the product. <strong>Find the product.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>

A)​ <strong>Find the product.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
B)​ <strong>Find the product.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
C)​ <strong>Find the product.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Find the product.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Find the product.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
سؤال
Find the product. Find the product.  <div style=padding-top: 35px>
سؤال
Read the method of solving the system of equations.​ ​ <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​   <div style=padding-top: 35px>
Solving the first equation for y , we have <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​   <div style=padding-top: 35px> . Substituting this value of y into the second equation, we have ​ <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​   <div style=padding-top: 35px>
The equation is quadratic. We write it in standard form and apply the quadratic formula. <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​   <div style=padding-top: 35px> <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​   <div style=padding-top: 35px> <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​   <div style=padding-top: 35px> <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​   <div style=padding-top: 35px>   <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​   <div style=padding-top: 35px>   <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​   <div style=padding-top: 35px>   <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​   <div style=padding-top: 35px>   ​ <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​   <div style=padding-top: 35px>
Use the method shown above to solve the system of equations. <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​   <div style=padding-top: 35px>

A)​ <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​   <div style=padding-top: 35px>
B)​ <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​   <div style=padding-top: 35px>
C) <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​   <div style=padding-top: 35px>
سؤال
Find the quotient. Write the answer in standard form for complex numbers. <strong>Find the quotient. Write the answer in standard form for complex numbers.   ​</strong> A)​   B)​   C)   D)​   E)​   <div style=padding-top: 35px>

A)​ <strong>Find the quotient. Write the answer in standard form for complex numbers.   ​</strong> A)​   B)​   C)   D)​   E)​   <div style=padding-top: 35px>
B)​ <strong>Find the quotient. Write the answer in standard form for complex numbers.   ​</strong> A)​   B)​   C)   D)​   E)​   <div style=padding-top: 35px>
C) <strong>Find the quotient. Write the answer in standard form for complex numbers.   ​</strong> A)​   B)​   C)   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Find the quotient. Write the answer in standard form for complex numbers.   ​</strong> A)​   B)​   C)   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Find the quotient. Write the answer in standard form for complex numbers.   ​</strong> A)​   B)​   C)   D)​   E)​   <div style=padding-top: 35px>
سؤال
Write the expression <strong>Write the expression    in terms of i and then simplify. ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>  in terms of i and then simplify. ​

A)​ <strong>Write the expression    in terms of i and then simplify. ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
B)​ <strong>Write the expression    in terms of i and then simplify. ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
C)​ <strong>Write the expression    in terms of i and then simplify. ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Write the expression    in terms of i and then simplify. ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Write the expression    in terms of i and then simplify. ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
سؤال
Find all x and y between 0 and <strong>Find all x and y between 0 and    so that the equation is true. ​   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>  so that the equation is true. ​ <strong>Find all x and y between 0 and    so that the equation is true. ​   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>

A) <strong>Find all x and y between 0 and    so that the equation is true. ​   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
B)​ <strong>Find all x and y between 0 and    so that the equation is true. ​   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
C)​ <strong>Find all x and y between 0 and    so that the equation is true. ​   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Find all x and y between 0 and    so that the equation is true. ​   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Find all x and y between 0 and    so that the equation is true. ​   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
سؤال
Write the expression Write the expression    in terms of i and then simplify.<div style=padding-top: 35px>  in terms of i and then simplify.
سؤال
Write the expression Write the expression    in terms of i .<div style=padding-top: 35px>  in terms of i .
سؤال
Graph the complex number and give the absolute value of the number. <strong>Graph the complex number and give the absolute value of the number.   ​</strong> A)​   B)​   C)​   D)​ ​   E)​   <div style=padding-top: 35px>

A)​ <strong>Graph the complex number and give the absolute value of the number.   ​</strong> A)​   B)​   C)​   D)​ ​   E)​   <div style=padding-top: 35px>
B)​ <strong>Graph the complex number and give the absolute value of the number.   ​</strong> A)​   B)​   C)​   D)​ ​   E)​   <div style=padding-top: 35px>
C)​ <strong>Graph the complex number and give the absolute value of the number.   ​</strong> A)​   B)​   C)​   D)​ ​   E)​   <div style=padding-top: 35px>
D)​ ​ <strong>Graph the complex number and give the absolute value of the number.   ​</strong> A)​   B)​   C)​   D)​ ​   E)​   <div style=padding-top: 35px>
E)​ <strong>Graph the complex number and give the absolute value of the number.   ​</strong> A)​   B)​   C)​   D)​ ​   E)​   <div style=padding-top: 35px>
سؤال
Show that Show that    is a solution to the equation   .<div style=padding-top: 35px>  is a solution to the equation Show that    is a solution to the equation   .<div style=padding-top: 35px> .
سؤال
Combine the complex numbers. Combine the complex numbers.  <div style=padding-top: 35px>
سؤال
Combine the complex numbers. Combine the complex numbers.  <div style=padding-top: 35px>
سؤال
Graph the number along with its opposite and conjugate. <strong>Graph the number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>

A)​ <strong>Graph the number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
B)​ <strong>Graph the number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
C)​ <strong>Graph the number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Graph the number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Graph the number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
سؤال
Find the quotient. Write the answer in standard form for complex numbers. Find the quotient. Write the answer in standard form for complex numbers.  <div style=padding-top: 35px>
سؤال
Find the product. Find the product.  <div style=padding-top: 35px>
سؤال
Write the complex number in standard form. <strong>Write the complex number in standard form.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>

A) <strong>Write the complex number in standard form.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
B)​ <strong>Write the complex number in standard form.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
C)​ <strong>Write the complex number in standard form.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Write the complex number in standard form.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Write the complex number in standard form.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
سؤال
Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth. <strong>Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>

A) <strong>Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
B)​ <strong>Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
C)​ <strong>Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
سؤال
Let Let    and    and find   .  <div style=padding-top: 35px>  and Let    and    and find   .  <div style=padding-top: 35px>  and find Let    and    and find   .  <div style=padding-top: 35px> . Let    and    and find   .  <div style=padding-top: 35px>
سؤال
Write the complex number in standard form. <strong>Write the complex number in standard form.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>

A) <strong>Write the complex number in standard form.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
B)​ <strong>Write the complex number in standard form.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
C)​ <strong>Write the complex number in standard form.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Write the complex number in standard form.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Write the complex number in standard form.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
سؤال
Simplify the power of i . Simplify the power of i .  <div style=padding-top: 35px>
سؤال
Read the method of solving the system of equations.
Read the method of solving the system of equations. ​   ​ Solving the first equation for  y , we have    . Substituting this value of  y  into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​<div style=padding-top: 35px>
Solving the first equation for  y , we have  Read the method of solving the system of equations. ​   ​ Solving the first equation for  y , we have    . Substituting this value of  y  into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​<div style=padding-top: 35px> . Substituting this value of  y  into the second equation, we have ​ Read the method of solving the system of equations. ​   ​ Solving the first equation for  y , we have    . Substituting this value of  y  into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​<div style=padding-top: 35px>
The equation is quadratic. We write it in standard form and apply the quadratic formula. Read the method of solving the system of equations. ​   ​ Solving the first equation for  y , we have    . Substituting this value of  y  into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​<div style=padding-top: 35px> Read the method of solving the system of equations. ​   ​ Solving the first equation for  y , we have    . Substituting this value of  y  into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​<div style=padding-top: 35px> Read the method of solving the system of equations. ​   ​ Solving the first equation for  y , we have    . Substituting this value of  y  into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​<div style=padding-top: 35px> Read the method of solving the system of equations. ​   ​ Solving the first equation for  y , we have    . Substituting this value of  y  into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​<div style=padding-top: 35px>   Read the method of solving the system of equations. ​   ​ Solving the first equation for  y , we have    . Substituting this value of  y  into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​<div style=padding-top: 35px>   Read the method of solving the system of equations. ​   ​ Solving the first equation for  y , we have    . Substituting this value of  y  into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​<div style=padding-top: 35px>   Read the method of solving the system of equations. ​   ​ Solving the first equation for  y , we have    . Substituting this value of  y  into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​<div style=padding-top: 35px>   ​ Read the method of solving the system of equations. ​   ​ Solving the first equation for  y , we have    . Substituting this value of  y  into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​<div style=padding-top: 35px>
Use the method shown above to solve the system of equations. Read the method of solving the system of equations. ​   ​ Solving the first equation for  y , we have    . Substituting this value of  y  into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​<div style=padding-top: 35px>
سؤال
Graph the complex number and give the absolute value of it. <strong>Graph the complex number and give the absolute value of it.   ​</strong> A)​   ​ The absolute value is 11 B)​   ​ The absolute value is 14 C)​     ​ The absolute value is 11 D)​ ​   ​ The absolute value is 10 E)​   ​ The absolute value is 14 <div style=padding-top: 35px>

A)​ <strong>Graph the complex number and give the absolute value of it.   ​</strong> A)​   ​ The absolute value is 11 B)​   ​ The absolute value is 14 C)​     ​ The absolute value is 11 D)​ ​   ​ The absolute value is 10 E)​   ​ The absolute value is 14 <div style=padding-top: 35px>
The absolute value is 11
B)​ <strong>Graph the complex number and give the absolute value of it.   ​</strong> A)​   ​ The absolute value is 11 B)​   ​ The absolute value is 14 C)​     ​ The absolute value is 11 D)​ ​   ​ The absolute value is 10 E)​   ​ The absolute value is 14 <div style=padding-top: 35px>
The absolute value is 14
C)​ <strong>Graph the complex number and give the absolute value of it.   ​</strong> A)​   ​ The absolute value is 11 B)​   ​ The absolute value is 14 C)​     ​ The absolute value is 11 D)​ ​   ​ The absolute value is 10 E)​   ​ The absolute value is 14 <div style=padding-top: 35px>   ​
The absolute value is 11
D)​ ​ <strong>Graph the complex number and give the absolute value of it.   ​</strong> A)​   ​ The absolute value is 11 B)​   ​ The absolute value is 14 C)​     ​ The absolute value is 11 D)​ ​   ​ The absolute value is 10 E)​   ​ The absolute value is 14 <div style=padding-top: 35px>

The absolute value is 10
E)​ <strong>Graph the complex number and give the absolute value of it.   ​</strong> A)​   ​ The absolute value is 11 B)​   ​ The absolute value is 14 C)​     ​ The absolute value is 11 D)​ ​   ​ The absolute value is 10 E)​   ​ The absolute value is 14 <div style=padding-top: 35px>
The absolute value is 14
سؤال
Graph the complex number along with its opposite and conjugate. <strong>Graph the complex number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>

A)​ <strong>Graph the complex number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
B)​ <strong>Graph the complex number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
C)​ <strong>Graph the complex number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Graph the complex number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Graph the complex number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
سؤال
If z is a complex number, show that the sum of z and its conjugate is a real number.
سؤال
Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth. ​ <strong>Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth. ​   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>

A) <strong>Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth. ​   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
B)​ <strong>Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth. ​   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
C)​ <strong>Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth. ​   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth. ​   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth. ​   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
سؤال
Graph the complex number along with its opposite and conjugate. <strong>Graph the complex number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>

A)​ <strong>Graph the complex number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
B)​ <strong>Graph the complex number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
C)​ <strong>Graph the complex number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Graph the complex number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Graph the complex number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
سؤال
Find the product. Find the product.  <div style=padding-top: 35px>
سؤال
Find x and y (real numbers)so that the equation is true. Find x and y (real numbers)so that the equation is true.   ​   ​  <div style=padding-top: 35px> Find x and y (real numbers)so that the equation is true.   ​   ​  <div style=padding-top: 35px> Find x and y (real numbers)so that the equation is true.   ​   ​  <div style=padding-top: 35px>
سؤال
Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree. Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.  <div style=padding-top: 35px>
سؤال
Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ . <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>

A) <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
B)​ <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
C)​ <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
سؤال
Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree. <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>

A) <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
B)​ <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
C)​ <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
سؤال
Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree. Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.  <div style=padding-top: 35px>
سؤال
Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree. <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>

A) <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
B)​ <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
C)​ <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
سؤال
Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree. <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>

A)​ <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
B)​ <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
C)​ <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
سؤال
Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree. <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>

A) <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
B)​ <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
C)​ <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
سؤال
Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree. Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.  <div style=padding-top: 35px>
سؤال
Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ . <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>

A) <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
B)​ <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
C)​ <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
سؤال
Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree. Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.  <div style=padding-top: 35px>
سؤال
Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree. Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.  <div style=padding-top: 35px>
سؤال
Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree. <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>

A) <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
B)​ <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
C)​ <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
سؤال
Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ . Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .  <div style=padding-top: 35px>
سؤال
Write the complex number in standard form. Write the complex number in standard form.  <div style=padding-top: 35px>
سؤال
Write the complex number in standard form. Write the complex number in standard form.  <div style=padding-top: 35px>
سؤال
Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ . Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .  <div style=padding-top: 35px>
سؤال
Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ . <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>

A) <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
B)​ <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
C)​ <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
سؤال
Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree. <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>

A) <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
B)​ <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
C)​ <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
سؤال
Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree. Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.  <div style=padding-top: 35px>
سؤال
Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ . Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .  <div style=padding-top: 35px>
سؤال
Convert complex numbers to trigonometric form and then simplify the expression. Write the answer in standard form. <strong>Convert complex numbers to trigonometric form and then simplify the expression. Write the answer in standard form.   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>

A)​ <strong>Convert complex numbers to trigonometric form and then simplify the expression. Write the answer in standard form.   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>
B)​ <strong>Convert complex numbers to trigonometric form and then simplify the expression. Write the answer in standard form.   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>
C)​ <strong>Convert complex numbers to trigonometric form and then simplify the expression. Write the answer in standard form.   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>
D)​ <strong>Convert complex numbers to trigonometric form and then simplify the expression. Write the answer in standard form.   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>
E) <strong>Convert complex numbers to trigonometric form and then simplify the expression. Write the answer in standard form.   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>
سؤال
Use DeMoivre's Theorem to find the following. Write your answer in standard form. Use DeMoivre's Theorem to find the following. Write your answer in standard form.  <div style=padding-top: 35px>
سؤال
Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth. Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth.  <div style=padding-top: 35px>
سؤال
Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​ <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​</strong> A)​-8 - 8 ​i ​   B)​1 8 i 1 1 1 1 11 C)​-​16 - 16 i   D)​116    + 16 i ​1 E)​8111 1 ​1 <div style=padding-top: 35px>

A)​-8 - 8 ​i ​ <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​</strong> A)​-8 - 8 ​i ​   B)​1 8 i 1 1 1 1 11 C)​-​16 - 16 i   D)​116    + 16 i ​1 E)​8111 1 ​1 <div style=padding-top: 35px>
B)​1 8 i 1 1 1 1 11
C)​-​16 - 16 i <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​</strong> A)​-8 - 8 ​i ​   B)​1 8 i 1 1 1 1 11 C)​-​16 - 16 i   D)​116    + 16 i ​1 E)​8111 1 ​1 <div style=padding-top: 35px>
D)​116 <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​</strong> A)​-8 - 8 ​i ​   B)​1 8 i 1 1 1 1 11 C)​-​16 - 16 i   D)​116    + 16 i ​1 E)​8111 1 ​1 <div style=padding-top: 35px>  + 16 i ​1
E)​8111 1 ​1
سؤال
Multiply. Leave the answer in trigonometric form. <strong>Multiply. Leave the answer in trigonometric form.     ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>   ​

A)​ <strong>Multiply. Leave the answer in trigonometric form.     ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
B)​ <strong>Multiply. Leave the answer in trigonometric form.     ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
C)​ <strong>Multiply. Leave the answer in trigonometric form.     ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Multiply. Leave the answer in trigonometric form.     ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Multiply. Leave the answer in trigonometric form.     ​</strong> A)​   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
سؤال
Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​ <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​</strong> A)   B)​   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​</strong> A)   B)​   C)   D)   E)   <div style=padding-top: 35px>
B)​ <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​</strong> A)   B)​   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​</strong> A)   B)​   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​</strong> A)   B)​   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​</strong> A)   B)​   C)   D)   E)   <div style=padding-top: 35px>
سؤال
DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)​   E)   <div style=padding-top: 35px> , which can be expressed as <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)​   E)   <div style=padding-top: 35px> Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​ <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)​   E)   <div style=padding-top: 35px>

A) <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)​   E)   <div style=padding-top: 35px>
B) <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)​   E)   <div style=padding-top: 35px>
C) <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)​   E)   <div style=padding-top: 35px>
D)​ <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)​   E)   <div style=padding-top: 35px>
E) <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)​   E)   <div style=padding-top: 35px>
سؤال
Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​ <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​</strong> A)​64 B)​-16    + 16 ​i C)​-8111 i ​1 D)​-16   + 16 ​i ​1 E)​-8 - 8 i ​   <div style=padding-top: 35px>

A)​64
B)​-16 <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​</strong> A)​64 B)​-16    + 16 ​i C)​-8111 i ​1 D)​-16   + 16 ​i ​1 E)​-8 - 8 i ​   <div style=padding-top: 35px>  + 16 ​i
C)​-8111 i ​1
D)​-16 <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​</strong> A)​64 B)​-16    + 16 ​i C)​-8111 i ​1 D)​-16   + 16 ​i ​1 E)​-8 - 8 i ​   <div style=padding-top: 35px> + 16 ​i ​1
E)​-8 - 8 i ​ <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​</strong> A)​64 B)​-16    + 16 ​i C)​-8111 i ​1 D)​-16   + 16 ​i ​1 E)​-8 - 8 i ​   <div style=padding-top: 35px>
سؤال
Write <strong>Write    and    in trigonometric form and find their product. ​   ​</strong> A)​   B)   C)​   D)​   E)​   <div style=padding-top: 35px>  and <strong>Write    and    in trigonometric form and find their product. ​   ​</strong> A)​   B)   C)​   D)​   E)​   <div style=padding-top: 35px>  in trigonometric form and find their product. ​ <strong>Write    and    in trigonometric form and find their product. ​   ​</strong> A)​   B)   C)​   D)​   E)​   <div style=padding-top: 35px>

A)​ <strong>Write    and    in trigonometric form and find their product. ​   ​</strong> A)​   B)   C)​   D)​   E)​   <div style=padding-top: 35px>
B) <strong>Write    and    in trigonometric form and find their product. ​   ​</strong> A)​   B)   C)​   D)​   E)​   <div style=padding-top: 35px>
C)​ <strong>Write    and    in trigonometric form and find their product. ​   ​</strong> A)​   B)   C)​   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Write    and    in trigonometric form and find their product. ​   ​</strong> A)​   B)   C)​   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Write    and    in trigonometric form and find their product. ​   ​</strong> A)​   B)   C)​   D)​   E)​   <div style=padding-top: 35px>
سؤال
Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth. Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth.  <div style=padding-top: 35px>
سؤال
Use DeMoivre's Theorem to find the following. Write your answer in standard form. <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form.     ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>   ​

A) <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form.     ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form.     ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form.     ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form.     ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form.     ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Divide. Leave your answer in trigonometric form. ​ <strong>Divide. Leave your answer in trigonometric form. ​   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>

A)​ <strong>Divide. Leave your answer in trigonometric form. ​   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>
B)​ <strong>Divide. Leave your answer in trigonometric form. ​   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>
C)​ <strong>Divide. Leave your answer in trigonometric form. ​   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>
D)​ <strong>Divide. Leave your answer in trigonometric form. ​   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>
E) <strong>Divide. Leave your answer in trigonometric form. ​   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>
سؤال
Find the quotient <strong>Find the quotient    in standard form.   ,    ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>  in standard form. <strong>Find the quotient    in standard form.   ,    ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px> <strong>Find the quotient    in standard form.   ,    ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>

A) <strong>Find the quotient    in standard form.   ,    ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
B)​ <strong>Find the quotient    in standard form.   ,    ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
C)​ <strong>Find the quotient    in standard form.   ,    ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Find the quotient    in standard form.   ,    ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Find the quotient    in standard form.   ,    ​</strong> A)   B)​   C)​   D)​   E)​   <div style=padding-top: 35px>
سؤال
DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> , which can be expressed as <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​ <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the product <strong>Find the product    in standard form.   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>  in standard form. <strong>Find the product    in standard form.   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>

A)​ <strong>Find the product    in standard form.   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>
B)​ <strong>Find the product    in standard form.   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>
C)​ <strong>Find the product    in standard form.   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>
D)​ <strong>Find the product    in standard form.   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>
E) <strong>Find the product    in standard form.   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>
سؤال
Divide. Leave your answer in trigonometric form. <strong>Divide. Leave your answer in trigonometric form.   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>

A)​ <strong>Divide. Leave your answer in trigonometric form.   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>
B)​ <strong>Divide. Leave your answer in trigonometric form.   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>
C)​ <strong>Divide. Leave your answer in trigonometric form.   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>
D)​ <strong>Divide. Leave your answer in trigonometric form.   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>
E) <strong>Divide. Leave your answer in trigonometric form.   ​</strong> A)​   B)​   C)​   D)​   E)   <div style=padding-top: 35px>
سؤال
Multiply. Leave the answer in trigonometric form. <strong>Multiply. Leave the answer in trigonometric form.   ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Multiply. Leave the answer in trigonometric form.   ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Multiply. Leave the answer in trigonometric form.   ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Multiply. Leave the answer in trigonometric form.   ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Multiply. Leave the answer in trigonometric form.   ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Multiply. Leave the answer in trigonometric form.   ​</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Multiply. Leave the answer in trigonometric form. <strong>Multiply. Leave the answer in trigonometric form.     ​</strong> A)​   B)   C)​   D)​   E)​   <div style=padding-top: 35px>   ​

A)​ <strong>Multiply. Leave the answer in trigonometric form.     ​</strong> A)​   B)   C)​   D)​   E)​   <div style=padding-top: 35px>
B) <strong>Multiply. Leave the answer in trigonometric form.     ​</strong> A)​   B)   C)​   D)​   E)​   <div style=padding-top: 35px>
C)​ <strong>Multiply. Leave the answer in trigonometric form.     ​</strong> A)​   B)   C)​   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Multiply. Leave the answer in trigonometric form.     ​</strong> A)​   B)   C)​   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Multiply. Leave the answer in trigonometric form.     ​</strong> A)​   B)   C)​   D)​   E)​   <div style=padding-top: 35px>
سؤال
Write <strong>Write    and    in trigonometric form and find their product.     ​</strong> A)​   B)   C)​   D)​   E)​   <div style=padding-top: 35px>  and <strong>Write    and    in trigonometric form and find their product.     ​</strong> A)​   B)   C)​   D)​   E)​   <div style=padding-top: 35px>  in trigonometric form and find their product. <strong>Write    and    in trigonometric form and find their product.     ​</strong> A)​   B)   C)​   D)​   E)​   <div style=padding-top: 35px>   ​

A)​ <strong>Write    and    in trigonometric form and find their product.     ​</strong> A)​   B)   C)​   D)​   E)​   <div style=padding-top: 35px>
B) <strong>Write    and    in trigonometric form and find their product.     ​</strong> A)​   B)   C)​   D)​   E)​   <div style=padding-top: 35px>
C)​ <strong>Write    and    in trigonometric form and find their product.     ​</strong> A)​   B)   C)​   D)​   E)​   <div style=padding-top: 35px>
D)​ <strong>Write    and    in trigonometric form and find their product.     ​</strong> A)​   B)   C)​   D)​   E)​   <div style=padding-top: 35px>
E)​ <strong>Write    and    in trigonometric form and find their product.     ​</strong> A)​   B)   C)​   D)​   E)​   <div style=padding-top: 35px>
سؤال
Write <strong>Write    and    in trigonometric form and then find their quotient. ​   ​</strong> A)​   B)​   C)​   D)   E)​   <div style=padding-top: 35px>  and <strong>Write    and    in trigonometric form and then find their quotient. ​   ​</strong> A)​   B)​   C)​   D)   E)​   <div style=padding-top: 35px>  in trigonometric form and then find their quotient. ​ <strong>Write    and    in trigonometric form and then find their quotient. ​   ​</strong> A)​   B)​   C)​   D)   E)​   <div style=padding-top: 35px>

A)​ <strong>Write    and    in trigonometric form and then find their quotient. ​   ​</strong> A)​   B)​   C)​   D)   E)​   <div style=padding-top: 35px>
B)​ <strong>Write    and    in trigonometric form and then find their quotient. ​   ​</strong> A)​   B)​   C)​   D)   E)​   <div style=padding-top: 35px>
C)​ <strong>Write    and    in trigonometric form and then find their quotient. ​   ​</strong> A)​   B)​   C)​   D)   E)​   <div style=padding-top: 35px>
D) <strong>Write    and    in trigonometric form and then find their quotient. ​   ​</strong> A)​   B)​   C)​   D)   E)​   <div style=padding-top: 35px>
E)​ <strong>Write    and    in trigonometric form and then find their quotient. ​   ​</strong> A)​   B)​   C)​   D)   E)​   <div style=padding-top: 35px>
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Deck 8: Complex Numbers and Polar Coordinates
1
Combine the complex numbers. <strong>Combine the complex numbers.   ​</strong> A)​   B)​   C)​   D)​   E)​

A)​ <strong>Combine the complex numbers.   ​</strong> A)​   B)​   C)​   D)​   E)​
B)​ <strong>Combine the complex numbers.   ​</strong> A)​   B)​   C)​   D)​   E)​
C)​ <strong>Combine the complex numbers.   ​</strong> A)​   B)​   C)​   D)​   E)​
D)​ <strong>Combine the complex numbers.   ​</strong> A)​   B)​   C)​   D)​   E)​
E)​ <strong>Combine the complex numbers.   ​</strong> A)​   B)​   C)​   D)​   E)​
​
2
Find the product. <strong>Find the product.   ​</strong> A)   B)   C)   D)   E)

A) <strong>Find the product.   ​</strong> A)   B)   C)   D)   E)
B) <strong>Find the product.   ​</strong> A)   B)   C)   D)   E)
C) <strong>Find the product.   ​</strong> A)   B)   C)   D)   E)
D) <strong>Find the product.   ​</strong> A)   B)   C)   D)   E)
E) <strong>Find the product.   ​</strong> A)   B)   C)   D)   E)
3
Find the product. <strong>Find the product.   ​</strong> A)​   B)​   C)   D)   E)​

A)​ <strong>Find the product.   ​</strong> A)​   B)​   C)   D)   E)​
B)​ <strong>Find the product.   ​</strong> A)​   B)​   C)   D)   E)​
C) <strong>Find the product.   ​</strong> A)​   B)​   C)   D)   E)​
D) <strong>Find the product.   ​</strong> A)​   B)​   C)   D)   E)​
E)​ <strong>Find the product.   ​</strong> A)​   B)​   C)   D)   E)​
4
Is <strong>Is    a solution to the equation   ? ​</strong> A)no B)yes  a solution to the equation <strong>Is    a solution to the equation   ? ​</strong> A)no B)yes ? ​

A)no
B)yes
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5
Let <strong>Let    and    and find   . ​</strong> A)   B)   C)​   D)​   E)​    and <strong>Let    and    and find   . ​</strong> A)   B)   C)​   D)​   E)​    and find <strong>Let    and    and find   . ​</strong> A)   B)   C)​   D)​   E)​   . ​

A) <strong>Let    and    and find   . ​</strong> A)   B)   C)​   D)​   E)​
B) <strong>Let    and    and find   . ​</strong> A)   B)   C)​   D)​   E)​
C)​ <strong>Let    and    and find   . ​</strong> A)   B)   C)​   D)​   E)​
D)​ <strong>Let    and    and find   . ​</strong> A)   B)   C)​   D)​   E)​
E)​ <strong>Let    and    and find   . ​</strong> A)   B)   C)​   D)​   E)​
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6
Let <strong>Let    and    and find   . ​</strong> A)   B)   C)   D)   E)    and <strong>Let    and    and find   . ​</strong> A)   B)   C)   D)   E)    and find <strong>Let    and    and find   . ​</strong> A)   B)   C)   D)   E)   . ​

A) <strong>Let    and    and find   . ​</strong> A)   B)   C)   D)   E)
B) <strong>Let    and    and find   . ​</strong> A)   B)   C)   D)   E)
C) <strong>Let    and    and find   . ​</strong> A)   B)   C)   D)   E)
D) <strong>Let    and    and find   . ​</strong> A)   B)   C)   D)   E)
E) <strong>Let    and    and find   . ​</strong> A)   B)   C)   D)   E)
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7
Combine the complex numbers. <strong>Combine the complex numbers.   ​</strong> A)   B)​   C)​   D)​   E)​

A) <strong>Combine the complex numbers.   ​</strong> A)   B)​   C)​   D)​   E)​
B)​ <strong>Combine the complex numbers.   ​</strong> A)   B)​   C)​   D)​   E)​
C)​ <strong>Combine the complex numbers.   ​</strong> A)   B)​   C)​   D)​   E)​
D)​ <strong>Combine the complex numbers.   ​</strong> A)   B)​   C)​   D)​   E)​
E)​ <strong>Combine the complex numbers.   ​</strong> A)   B)​   C)​   D)​   E)​
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8
Write the expression <strong>Write the expression    in terms of i.</strong> A)​   B)​   C)​   D)​   E)​    in terms of i.

A)​ <strong>Write the expression    in terms of i.</strong> A)​   B)​   C)​   D)​   E)​
B)​ <strong>Write the expression    in terms of i.</strong> A)​   B)​   C)​   D)​   E)​
C)​ <strong>Write the expression    in terms of i.</strong> A)​   B)​   C)​   D)​   E)​
D)​ <strong>Write the expression    in terms of i.</strong> A)​   B)​   C)​   D)​   E)​
E)​ <strong>Write the expression    in terms of i.</strong> A)​   B)​   C)​   D)​   E)​
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9
Simplify the power of i . ​ <strong>Simplify the power of i . ​   ​</strong> A)   B)   C)   D)   E)

A) <strong>Simplify the power of i . ​   ​</strong> A)   B)   C)   D)   E)
B) <strong>Simplify the power of i . ​   ​</strong> A)   B)   C)   D)   E)
C) <strong>Simplify the power of i . ​   ​</strong> A)   B)   C)   D)   E)
D) <strong>Simplify the power of i . ​   ​</strong> A)   B)   C)   D)   E)
E) <strong>Simplify the power of i . ​   ​</strong> A)   B)   C)   D)   E)
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10
Find x and y (real numbers)so that the equation is true. <strong>Find x and y (real numbers)so that the equation is true.   ​</strong> A)​   B)​   C)​   D)​   E)

A)​ <strong>Find x and y (real numbers)so that the equation is true.   ​</strong> A)​   B)​   C)​   D)​   E)
B)​ <strong>Find x and y (real numbers)so that the equation is true.   ​</strong> A)​   B)​   C)​   D)​   E)
C)​ <strong>Find x and y (real numbers)so that the equation is true.   ​</strong> A)​   B)​   C)​   D)​   E)
D)​ <strong>Find x and y (real numbers)so that the equation is true.   ​</strong> A)​   B)​   C)​   D)​   E)
E) <strong>Find x and y (real numbers)so that the equation is true.   ​</strong> A)​   B)​   C)​   D)​   E)
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11
If z is a complex number then the product of z and its conjugate is a real number. ​

A)false
B)true
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12
Let Let    and    and find   .   and Let    and    and find   .   and find Let    and    and find   .  . Let    and    and find   .
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13
Find the product. <strong>Find the product.   ​</strong> A)​   B)​   C)​   D)​   E)​

A)​ <strong>Find the product.   ​</strong> A)​   B)​   C)​   D)​   E)​
B)​ <strong>Find the product.   ​</strong> A)​   B)​   C)​   D)​   E)​
C)​ <strong>Find the product.   ​</strong> A)​   B)​   C)​   D)​   E)​
D)​ <strong>Find the product.   ​</strong> A)​   B)​   C)​   D)​   E)​
E)​ <strong>Find the product.   ​</strong> A)​   B)​   C)​   D)​   E)​
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14
Find the product. Find the product.
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15
Read the method of solving the system of equations.​ ​ <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​
Solving the first equation for y , we have <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​   . Substituting this value of y into the second equation, we have ​ <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​
The equation is quadratic. We write it in standard form and apply the quadratic formula. <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​   <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​   <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​   <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​     <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​     <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​     <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​     ​ <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​
Use the method shown above to solve the system of equations. <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​

A)​ <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​
B)​ <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​
C) <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​
D)​ <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​
E)​ <strong>Read the method of solving the system of equations.​ ​   ​ Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​</strong> A)​   B)​   C)   D)​   E)​
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16
Find the quotient. Write the answer in standard form for complex numbers. <strong>Find the quotient. Write the answer in standard form for complex numbers.   ​</strong> A)​   B)​   C)   D)​   E)​

A)​ <strong>Find the quotient. Write the answer in standard form for complex numbers.   ​</strong> A)​   B)​   C)   D)​   E)​
B)​ <strong>Find the quotient. Write the answer in standard form for complex numbers.   ​</strong> A)​   B)​   C)   D)​   E)​
C) <strong>Find the quotient. Write the answer in standard form for complex numbers.   ​</strong> A)​   B)​   C)   D)​   E)​
D)​ <strong>Find the quotient. Write the answer in standard form for complex numbers.   ​</strong> A)​   B)​   C)   D)​   E)​
E)​ <strong>Find the quotient. Write the answer in standard form for complex numbers.   ​</strong> A)​   B)​   C)   D)​   E)​
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17
Write the expression <strong>Write the expression    in terms of i and then simplify. ​</strong> A)​   B)​   C)​   D)​   E)​    in terms of i and then simplify. ​

A)​ <strong>Write the expression    in terms of i and then simplify. ​</strong> A)​   B)​   C)​   D)​   E)​
B)​ <strong>Write the expression    in terms of i and then simplify. ​</strong> A)​   B)​   C)​   D)​   E)​
C)​ <strong>Write the expression    in terms of i and then simplify. ​</strong> A)​   B)​   C)​   D)​   E)​
D)​ <strong>Write the expression    in terms of i and then simplify. ​</strong> A)​   B)​   C)​   D)​   E)​
E)​ <strong>Write the expression    in terms of i and then simplify. ​</strong> A)​   B)​   C)​   D)​   E)​
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18
Find all x and y between 0 and <strong>Find all x and y between 0 and    so that the equation is true. ​   ​</strong> A)   B)​   C)​   D)​   E)​    so that the equation is true. ​ <strong>Find all x and y between 0 and    so that the equation is true. ​   ​</strong> A)   B)​   C)​   D)​   E)​

A) <strong>Find all x and y between 0 and    so that the equation is true. ​   ​</strong> A)   B)​   C)​   D)​   E)​
B)​ <strong>Find all x and y between 0 and    so that the equation is true. ​   ​</strong> A)   B)​   C)​   D)​   E)​
C)​ <strong>Find all x and y between 0 and    so that the equation is true. ​   ​</strong> A)   B)​   C)​   D)​   E)​
D)​ <strong>Find all x and y between 0 and    so that the equation is true. ​   ​</strong> A)   B)​   C)​   D)​   E)​
E)​ <strong>Find all x and y between 0 and    so that the equation is true. ​   ​</strong> A)   B)​   C)​   D)​   E)​
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19
Write the expression Write the expression    in terms of i and then simplify.  in terms of i and then simplify.
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20
Write the expression Write the expression    in terms of i .  in terms of i .
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21
Graph the complex number and give the absolute value of the number. <strong>Graph the complex number and give the absolute value of the number.   ​</strong> A)​   B)​   C)​   D)​ ​   E)​

A)​ <strong>Graph the complex number and give the absolute value of the number.   ​</strong> A)​   B)​   C)​   D)​ ​   E)​
B)​ <strong>Graph the complex number and give the absolute value of the number.   ​</strong> A)​   B)​   C)​   D)​ ​   E)​
C)​ <strong>Graph the complex number and give the absolute value of the number.   ​</strong> A)​   B)​   C)​   D)​ ​   E)​
D)​ ​ <strong>Graph the complex number and give the absolute value of the number.   ​</strong> A)​   B)​   C)​   D)​ ​   E)​
E)​ <strong>Graph the complex number and give the absolute value of the number.   ​</strong> A)​   B)​   C)​   D)​ ​   E)​
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22
Show that Show that    is a solution to the equation   .  is a solution to the equation Show that    is a solution to the equation   . .
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23
Combine the complex numbers. Combine the complex numbers.
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24
Combine the complex numbers. Combine the complex numbers.
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25
Graph the number along with its opposite and conjugate. <strong>Graph the number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​

A)​ <strong>Graph the number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​
B)​ <strong>Graph the number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​
C)​ <strong>Graph the number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​
D)​ <strong>Graph the number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​
E)​ <strong>Graph the number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​
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افتح القفل للوصول البطاقات البالغ عددها 177 في هذه المجموعة.
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26
Find the quotient. Write the answer in standard form for complex numbers. Find the quotient. Write the answer in standard form for complex numbers.
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افتح القفل للوصول البطاقات البالغ عددها 177 في هذه المجموعة.
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27
Find the product. Find the product.
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افتح القفل للوصول البطاقات البالغ عددها 177 في هذه المجموعة.
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28
Write the complex number in standard form. <strong>Write the complex number in standard form.   ​</strong> A)   B)​   C)​   D)​   E)​

A) <strong>Write the complex number in standard form.   ​</strong> A)   B)​   C)​   D)​   E)​
B)​ <strong>Write the complex number in standard form.   ​</strong> A)   B)​   C)​   D)​   E)​
C)​ <strong>Write the complex number in standard form.   ​</strong> A)   B)​   C)​   D)​   E)​
D)​ <strong>Write the complex number in standard form.   ​</strong> A)   B)​   C)​   D)​   E)​
E)​ <strong>Write the complex number in standard form.   ​</strong> A)   B)​   C)​   D)​   E)​
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افتح القفل للوصول البطاقات البالغ عددها 177 في هذه المجموعة.
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29
Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth. <strong>Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth.   ​</strong> A)   B)​   C)​   D)​   E)​

A) <strong>Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth.   ​</strong> A)   B)​   C)​   D)​   E)​
B)​ <strong>Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth.   ​</strong> A)   B)​   C)​   D)​   E)​
C)​ <strong>Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth.   ​</strong> A)   B)​   C)​   D)​   E)​
D)​ <strong>Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth.   ​</strong> A)   B)​   C)​   D)​   E)​
E)​ <strong>Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth.   ​</strong> A)   B)​   C)​   D)​   E)​
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افتح القفل للوصول البطاقات البالغ عددها 177 في هذه المجموعة.
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30
Let Let    and    and find   .   and Let    and    and find   .   and find Let    and    and find   .  . Let    and    and find   .
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افتح القفل للوصول البطاقات البالغ عددها 177 في هذه المجموعة.
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31
Write the complex number in standard form. <strong>Write the complex number in standard form.   ​</strong> A)   B)​   C)​   D)​   E)​

A) <strong>Write the complex number in standard form.   ​</strong> A)   B)​   C)​   D)​   E)​
B)​ <strong>Write the complex number in standard form.   ​</strong> A)   B)​   C)​   D)​   E)​
C)​ <strong>Write the complex number in standard form.   ​</strong> A)   B)​   C)​   D)​   E)​
D)​ <strong>Write the complex number in standard form.   ​</strong> A)   B)​   C)​   D)​   E)​
E)​ <strong>Write the complex number in standard form.   ​</strong> A)   B)​   C)​   D)​   E)​
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افتح القفل للوصول البطاقات البالغ عددها 177 في هذه المجموعة.
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32
Simplify the power of i . Simplify the power of i .
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افتح القفل للوصول البطاقات البالغ عددها 177 في هذه المجموعة.
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33
Read the method of solving the system of equations.
Read the method of solving the system of equations. ​   ​ Solving the first equation for  y , we have    . Substituting this value of  y  into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​
Solving the first equation for  y , we have  Read the method of solving the system of equations. ​   ​ Solving the first equation for  y , we have    . Substituting this value of  y  into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​ . Substituting this value of  y  into the second equation, we have ​ Read the method of solving the system of equations. ​   ​ Solving the first equation for  y , we have    . Substituting this value of  y  into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​
The equation is quadratic. We write it in standard form and apply the quadratic formula. Read the method of solving the system of equations. ​   ​ Solving the first equation for  y , we have    . Substituting this value of  y  into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​Read the method of solving the system of equations. ​   ​ Solving the first equation for  y , we have    . Substituting this value of  y  into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​Read the method of solving the system of equations. ​   ​ Solving the first equation for  y , we have    . Substituting this value of  y  into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​ Read the method of solving the system of equations. ​   ​ Solving the first equation for  y , we have    . Substituting this value of  y  into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​   Read the method of solving the system of equations. ​   ​ Solving the first equation for  y , we have    . Substituting this value of  y  into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​   Read the method of solving the system of equations. ​   ​ Solving the first equation for  y , we have    . Substituting this value of  y  into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​   Read the method of solving the system of equations. ​   ​ Solving the first equation for  y , we have    . Substituting this value of  y  into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​   ​ Read the method of solving the system of equations. ​   ​ Solving the first equation for  y , we have    . Substituting this value of  y  into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​
Use the method shown above to solve the system of equations. Read the method of solving the system of equations. ​   ​ Solving the first equation for  y , we have    . Substituting this value of  y  into the second equation, we have ​   ​ The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​ Use the method shown above to solve the system of equations.   ​
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افتح القفل للوصول البطاقات البالغ عددها 177 في هذه المجموعة.
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34
Graph the complex number and give the absolute value of it. <strong>Graph the complex number and give the absolute value of it.   ​</strong> A)​   ​ The absolute value is 11 B)​   ​ The absolute value is 14 C)​     ​ The absolute value is 11 D)​ ​   ​ The absolute value is 10 E)​   ​ The absolute value is 14

A)​ <strong>Graph the complex number and give the absolute value of it.   ​</strong> A)​   ​ The absolute value is 11 B)​   ​ The absolute value is 14 C)​     ​ The absolute value is 11 D)​ ​   ​ The absolute value is 10 E)​   ​ The absolute value is 14
The absolute value is 11
B)​ <strong>Graph the complex number and give the absolute value of it.   ​</strong> A)​   ​ The absolute value is 11 B)​   ​ The absolute value is 14 C)​     ​ The absolute value is 11 D)​ ​   ​ The absolute value is 10 E)​   ​ The absolute value is 14
The absolute value is 14
C)​ <strong>Graph the complex number and give the absolute value of it.   ​</strong> A)​   ​ The absolute value is 11 B)​   ​ The absolute value is 14 C)​     ​ The absolute value is 11 D)​ ​   ​ The absolute value is 10 E)​   ​ The absolute value is 14   ​
The absolute value is 11
D)​ ​ <strong>Graph the complex number and give the absolute value of it.   ​</strong> A)​   ​ The absolute value is 11 B)​   ​ The absolute value is 14 C)​     ​ The absolute value is 11 D)​ ​   ​ The absolute value is 10 E)​   ​ The absolute value is 14

The absolute value is 10
E)​ <strong>Graph the complex number and give the absolute value of it.   ​</strong> A)​   ​ The absolute value is 11 B)​   ​ The absolute value is 14 C)​     ​ The absolute value is 11 D)​ ​   ​ The absolute value is 10 E)​   ​ The absolute value is 14
The absolute value is 14
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افتح القفل للوصول البطاقات البالغ عددها 177 في هذه المجموعة.
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35
Graph the complex number along with its opposite and conjugate. <strong>Graph the complex number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​

A)​ <strong>Graph the complex number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​
B)​ <strong>Graph the complex number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​
C)​ <strong>Graph the complex number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​
D)​ <strong>Graph the complex number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​
E)​ <strong>Graph the complex number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​
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افتح القفل للوصول البطاقات البالغ عددها 177 في هذه المجموعة.
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36
If z is a complex number, show that the sum of z and its conjugate is a real number.
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افتح القفل للوصول البطاقات البالغ عددها 177 في هذه المجموعة.
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37
Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth. ​ <strong>Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth. ​   ​</strong> A)   B)​   C)​   D)​   E)​

A) <strong>Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth. ​   ​</strong> A)   B)​   C)​   D)​   E)​
B)​ <strong>Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth. ​   ​</strong> A)   B)​   C)​   D)​   E)​
C)​ <strong>Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth. ​   ​</strong> A)   B)​   C)​   D)​   E)​
D)​ <strong>Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth. ​   ​</strong> A)   B)​   C)​   D)​   E)​
E)​ <strong>Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth. ​   ​</strong> A)   B)​   C)​   D)​   E)​
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 177 في هذه المجموعة.
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38
Graph the complex number along with its opposite and conjugate. <strong>Graph the complex number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​

A)​ <strong>Graph the complex number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​
B)​ <strong>Graph the complex number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​
C)​ <strong>Graph the complex number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​
D)​ <strong>Graph the complex number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​
E)​ <strong>Graph the complex number along with its opposite and conjugate.   ​</strong> A)​   B)​   C)​   D)​   E)​
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افتح القفل للوصول البطاقات البالغ عددها 177 في هذه المجموعة.
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39
Find the product. Find the product.
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افتح القفل للوصول البطاقات البالغ عددها 177 في هذه المجموعة.
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40
Find x and y (real numbers)so that the equation is true. Find x and y (real numbers)so that the equation is true.   ​   ​  Find x and y (real numbers)so that the equation is true.   ​   ​  Find x and y (real numbers)so that the equation is true.   ​   ​
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افتح القفل للوصول البطاقات البالغ عددها 177 في هذه المجموعة.
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41
Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree. Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.
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افتح القفل للوصول البطاقات البالغ عددها 177 في هذه المجموعة.
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42
Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ . <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​

A) <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​
B)​ <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​
C)​ <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​
D)​ <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​
E)​ <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​
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افتح القفل للوصول البطاقات البالغ عددها 177 في هذه المجموعة.
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43
Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree. <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​

A) <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​
B)​ <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​
C)​ <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​
D)​ <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​
E)​ <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​
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افتح القفل للوصول البطاقات البالغ عددها 177 في هذه المجموعة.
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44
Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree. Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.
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افتح القفل للوصول البطاقات البالغ عددها 177 في هذه المجموعة.
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45
Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree. <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​

A) <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​
B)​ <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​
C)​ <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​
D)​ <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​
E)​ <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 177 في هذه المجموعة.
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46
Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree. <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)​   B)​   C)​   D)​   E)​

A)​ <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)​   B)​   C)​   D)​   E)​
B)​ <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)​   B)​   C)​   D)​   E)​
C)​ <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)​   B)​   C)​   D)​   E)​
D)​ <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)​   B)​   C)​   D)​   E)​
E)​ <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)​   B)​   C)​   D)​   E)​
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افتح القفل للوصول البطاقات البالغ عددها 177 في هذه المجموعة.
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47
Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree. <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​

A) <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​
B)​ <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​
C)​ <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​
D)​ <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​
E)​ <strong>Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 177 في هذه المجموعة.
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48
Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree. Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.
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افتح القفل للوصول البطاقات البالغ عددها 177 في هذه المجموعة.
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49
Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ . <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​

A) <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​
B)​ <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​
C)​ <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​
D)​ <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​
E)​ <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​
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افتح القفل للوصول البطاقات البالغ عددها 177 في هذه المجموعة.
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50
Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree. Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 177 في هذه المجموعة.
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51
Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree. Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 177 في هذه المجموعة.
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52
Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree. <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​

A) <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​
B)​ <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​
C)​ <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​
D)​ <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​
E)​ <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​
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53
Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ . Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .
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54
Write the complex number in standard form. Write the complex number in standard form.
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55
Write the complex number in standard form. Write the complex number in standard form.
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56
Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ . Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .
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57
Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ . <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​

A) <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​
B)​ <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​
C)​ <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​
D)​ <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​
E)​ <strong>Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​</strong> A)   B)​   C)​   D)​   E)​
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58
Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree. <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​

A) <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​
B)​ <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​
C)​ <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​
D)​ <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​
E)​ <strong>Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.   ​</strong> A)   B)​   C)​   D)​   E)​
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59
Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree. Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.
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افتح القفل للوصول البطاقات البالغ عددها 177 في هذه المجموعة.
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60
Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ . Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .
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61
Convert complex numbers to trigonometric form and then simplify the expression. Write the answer in standard form. <strong>Convert complex numbers to trigonometric form and then simplify the expression. Write the answer in standard form.   ​</strong> A)​   B)​   C)​   D)​   E)

A)​ <strong>Convert complex numbers to trigonometric form and then simplify the expression. Write the answer in standard form.   ​</strong> A)​   B)​   C)​   D)​   E)
B)​ <strong>Convert complex numbers to trigonometric form and then simplify the expression. Write the answer in standard form.   ​</strong> A)​   B)​   C)​   D)​   E)
C)​ <strong>Convert complex numbers to trigonometric form and then simplify the expression. Write the answer in standard form.   ​</strong> A)​   B)​   C)​   D)​   E)
D)​ <strong>Convert complex numbers to trigonometric form and then simplify the expression. Write the answer in standard form.   ​</strong> A)​   B)​   C)​   D)​   E)
E) <strong>Convert complex numbers to trigonometric form and then simplify the expression. Write the answer in standard form.   ​</strong> A)​   B)​   C)​   D)​   E)
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62
Use DeMoivre's Theorem to find the following. Write your answer in standard form. Use DeMoivre's Theorem to find the following. Write your answer in standard form.
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63
Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth. Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth.
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64
Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​ <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​</strong> A)​-8 - 8 ​i ​   B)​1 8 i 1 1 1 1 11 C)​-​16 - 16 i   D)​116    + 16 i ​1 E)​8111 1 ​1

A)​-8 - 8 ​i ​ <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​</strong> A)​-8 - 8 ​i ​   B)​1 8 i 1 1 1 1 11 C)​-​16 - 16 i   D)​116    + 16 i ​1 E)​8111 1 ​1
B)​1 8 i 1 1 1 1 11
C)​-​16 - 16 i <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​</strong> A)​-8 - 8 ​i ​   B)​1 8 i 1 1 1 1 11 C)​-​16 - 16 i   D)​116    + 16 i ​1 E)​8111 1 ​1
D)​116 <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​</strong> A)​-8 - 8 ​i ​   B)​1 8 i 1 1 1 1 11 C)​-​16 - 16 i   D)​116    + 16 i ​1 E)​8111 1 ​1  + 16 i ​1
E)​8111 1 ​1
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65
Multiply. Leave the answer in trigonometric form. <strong>Multiply. Leave the answer in trigonometric form.     ​</strong> A)​   B)​   C)​   D)​   E)​     ​

A)​ <strong>Multiply. Leave the answer in trigonometric form.     ​</strong> A)​   B)​   C)​   D)​   E)​
B)​ <strong>Multiply. Leave the answer in trigonometric form.     ​</strong> A)​   B)​   C)​   D)​   E)​
C)​ <strong>Multiply. Leave the answer in trigonometric form.     ​</strong> A)​   B)​   C)​   D)​   E)​
D)​ <strong>Multiply. Leave the answer in trigonometric form.     ​</strong> A)​   B)​   C)​   D)​   E)​
E)​ <strong>Multiply. Leave the answer in trigonometric form.     ​</strong> A)​   B)​   C)​   D)​   E)​
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66
Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​ <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​</strong> A)   B)​   C)   D)   E)

A) <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​</strong> A)   B)​   C)   D)   E)
B)​ <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​</strong> A)   B)​   C)   D)   E)
C) <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​</strong> A)   B)​   C)   D)   E)
D) <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​</strong> A)   B)​   C)   D)   E)
E) <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​</strong> A)   B)​   C)   D)   E)
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67
DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)​   E)   , which can be expressed as <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)​   E)   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​ <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)​   E)

A) <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)​   E)
B) <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)​   E)
C) <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)​   E)
D)​ <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)​   E)
E) <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)​   E)
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68
Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​ <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​</strong> A)​64 B)​-16    + 16 ​i C)​-8111 i ​1 D)​-16   + 16 ​i ​1 E)​-8 - 8 i ​

A)​64
B)​-16 <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​</strong> A)​64 B)​-16    + 16 ​i C)​-8111 i ​1 D)​-16   + 16 ​i ​1 E)​-8 - 8 i ​    + 16 ​i
C)​-8111 i ​1
D)​-16 <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​</strong> A)​64 B)​-16    + 16 ​i C)​-8111 i ​1 D)​-16   + 16 ​i ​1 E)​-8 - 8 i ​   + 16 ​i ​1
E)​-8 - 8 i ​ <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​</strong> A)​64 B)​-16    + 16 ​i C)​-8111 i ​1 D)​-16   + 16 ​i ​1 E)​-8 - 8 i ​
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69
Write <strong>Write    and    in trigonometric form and find their product. ​   ​</strong> A)​   B)   C)​   D)​   E)​    and <strong>Write    and    in trigonometric form and find their product. ​   ​</strong> A)​   B)   C)​   D)​   E)​    in trigonometric form and find their product. ​ <strong>Write    and    in trigonometric form and find their product. ​   ​</strong> A)​   B)   C)​   D)​   E)​

A)​ <strong>Write    and    in trigonometric form and find their product. ​   ​</strong> A)​   B)   C)​   D)​   E)​
B) <strong>Write    and    in trigonometric form and find their product. ​   ​</strong> A)​   B)   C)​   D)​   E)​
C)​ <strong>Write    and    in trigonometric form and find their product. ​   ​</strong> A)​   B)   C)​   D)​   E)​
D)​ <strong>Write    and    in trigonometric form and find their product. ​   ​</strong> A)​   B)   C)​   D)​   E)​
E)​ <strong>Write    and    in trigonometric form and find their product. ​   ​</strong> A)​   B)   C)​   D)​   E)​
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70
Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth. Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth.
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71
Use DeMoivre's Theorem to find the following. Write your answer in standard form. <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form.     ​</strong> A)   B)   C)   D)   E)     ​

A) <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form.     ​</strong> A)   B)   C)   D)   E)
B) <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form.     ​</strong> A)   B)   C)   D)   E)
C) <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form.     ​</strong> A)   B)   C)   D)   E)
D) <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form.     ​</strong> A)   B)   C)   D)   E)
E) <strong>Use DeMoivre's Theorem to find the following. Write your answer in standard form.     ​</strong> A)   B)   C)   D)   E)
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72
Divide. Leave your answer in trigonometric form. ​ <strong>Divide. Leave your answer in trigonometric form. ​   ​</strong> A)​   B)​   C)​   D)​   E)

A)​ <strong>Divide. Leave your answer in trigonometric form. ​   ​</strong> A)​   B)​   C)​   D)​   E)
B)​ <strong>Divide. Leave your answer in trigonometric form. ​   ​</strong> A)​   B)​   C)​   D)​   E)
C)​ <strong>Divide. Leave your answer in trigonometric form. ​   ​</strong> A)​   B)​   C)​   D)​   E)
D)​ <strong>Divide. Leave your answer in trigonometric form. ​   ​</strong> A)​   B)​   C)​   D)​   E)
E) <strong>Divide. Leave your answer in trigonometric form. ​   ​</strong> A)​   B)​   C)​   D)​   E)
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73
Find the quotient <strong>Find the quotient    in standard form.   ,    ​</strong> A)   B)​   C)​   D)​   E)​    in standard form. <strong>Find the quotient    in standard form.   ,    ​</strong> A)   B)​   C)​   D)​   E)​   <strong>Find the quotient    in standard form.   ,    ​</strong> A)   B)​   C)​   D)​   E)​

A) <strong>Find the quotient    in standard form.   ,    ​</strong> A)   B)​   C)​   D)​   E)​
B)​ <strong>Find the quotient    in standard form.   ,    ​</strong> A)   B)​   C)​   D)​   E)​
C)​ <strong>Find the quotient    in standard form.   ,    ​</strong> A)   B)​   C)​   D)​   E)​
D)​ <strong>Find the quotient    in standard form.   ,    ​</strong> A)   B)​   C)​   D)​   E)​
E)​ <strong>Find the quotient    in standard form.   ,    ​</strong> A)   B)​   C)​   D)​   E)​
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74
DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)   E)   , which can be expressed as <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)   E)   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​ <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)   E)

A) <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)   E)
B) <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)   E)
C) <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)   E)
D) <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)   E)
E) <strong>DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. ​   ​</strong> A)   B)   C)   D)   E)
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75
Find the product <strong>Find the product    in standard form.   ​</strong> A)​   B)​   C)​   D)​   E)    in standard form. <strong>Find the product    in standard form.   ​</strong> A)​   B)​   C)​   D)​   E)

A)​ <strong>Find the product    in standard form.   ​</strong> A)​   B)​   C)​   D)​   E)
B)​ <strong>Find the product    in standard form.   ​</strong> A)​   B)​   C)​   D)​   E)
C)​ <strong>Find the product    in standard form.   ​</strong> A)​   B)​   C)​   D)​   E)
D)​ <strong>Find the product    in standard form.   ​</strong> A)​   B)​   C)​   D)​   E)
E) <strong>Find the product    in standard form.   ​</strong> A)​   B)​   C)​   D)​   E)
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76
Divide. Leave your answer in trigonometric form. <strong>Divide. Leave your answer in trigonometric form.   ​</strong> A)​   B)​   C)​   D)​   E)

A)​ <strong>Divide. Leave your answer in trigonometric form.   ​</strong> A)​   B)​   C)​   D)​   E)
B)​ <strong>Divide. Leave your answer in trigonometric form.   ​</strong> A)​   B)​   C)​   D)​   E)
C)​ <strong>Divide. Leave your answer in trigonometric form.   ​</strong> A)​   B)​   C)​   D)​   E)
D)​ <strong>Divide. Leave your answer in trigonometric form.   ​</strong> A)​   B)​   C)​   D)​   E)
E) <strong>Divide. Leave your answer in trigonometric form.   ​</strong> A)​   B)​   C)​   D)​   E)
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77
Multiply. Leave the answer in trigonometric form. <strong>Multiply. Leave the answer in trigonometric form.   ​</strong> A)   B)   C)   D)   E)

A) <strong>Multiply. Leave the answer in trigonometric form.   ​</strong> A)   B)   C)   D)   E)
B) <strong>Multiply. Leave the answer in trigonometric form.   ​</strong> A)   B)   C)   D)   E)
C) <strong>Multiply. Leave the answer in trigonometric form.   ​</strong> A)   B)   C)   D)   E)
D) <strong>Multiply. Leave the answer in trigonometric form.   ​</strong> A)   B)   C)   D)   E)
E) <strong>Multiply. Leave the answer in trigonometric form.   ​</strong> A)   B)   C)   D)   E)
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Multiply. Leave the answer in trigonometric form. <strong>Multiply. Leave the answer in trigonometric form.     ​</strong> A)​   B)   C)​   D)​   E)​     ​

A)​ <strong>Multiply. Leave the answer in trigonometric form.     ​</strong> A)​   B)   C)​   D)​   E)​
B) <strong>Multiply. Leave the answer in trigonometric form.     ​</strong> A)​   B)   C)​   D)​   E)​
C)​ <strong>Multiply. Leave the answer in trigonometric form.     ​</strong> A)​   B)   C)​   D)​   E)​
D)​ <strong>Multiply. Leave the answer in trigonometric form.     ​</strong> A)​   B)   C)​   D)​   E)​
E)​ <strong>Multiply. Leave the answer in trigonometric form.     ​</strong> A)​   B)   C)​   D)​   E)​
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Write <strong>Write    and    in trigonometric form and find their product.     ​</strong> A)​   B)   C)​   D)​   E)​    and <strong>Write    and    in trigonometric form and find their product.     ​</strong> A)​   B)   C)​   D)​   E)​    in trigonometric form and find their product. <strong>Write    and    in trigonometric form and find their product.     ​</strong> A)​   B)   C)​   D)​   E)​     ​

A)​ <strong>Write    and    in trigonometric form and find their product.     ​</strong> A)​   B)   C)​   D)​   E)​
B) <strong>Write    and    in trigonometric form and find their product.     ​</strong> A)​   B)   C)​   D)​   E)​
C)​ <strong>Write    and    in trigonometric form and find their product.     ​</strong> A)​   B)   C)​   D)​   E)​
D)​ <strong>Write    and    in trigonometric form and find their product.     ​</strong> A)​   B)   C)​   D)​   E)​
E)​ <strong>Write    and    in trigonometric form and find their product.     ​</strong> A)​   B)   C)​   D)​   E)​
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Write <strong>Write    and    in trigonometric form and then find their quotient. ​   ​</strong> A)​   B)​   C)​   D)   E)​    and <strong>Write    and    in trigonometric form and then find their quotient. ​   ​</strong> A)​   B)​   C)​   D)   E)​    in trigonometric form and then find their quotient. ​ <strong>Write    and    in trigonometric form and then find their quotient. ​   ​</strong> A)​   B)​   C)​   D)   E)​

A)​ <strong>Write    and    in trigonometric form and then find their quotient. ​   ​</strong> A)​   B)​   C)​   D)   E)​
B)​ <strong>Write    and    in trigonometric form and then find their quotient. ​   ​</strong> A)​   B)​   C)​   D)   E)​
C)​ <strong>Write    and    in trigonometric form and then find their quotient. ​   ​</strong> A)​   B)​   C)​   D)   E)​
D) <strong>Write    and    in trigonometric form and then find their quotient. ​   ​</strong> A)​   B)​   C)​   D)   E)​
E)​ <strong>Write    and    in trigonometric form and then find their quotient. ​   ​</strong> A)​   B)​   C)​   D)   E)​
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