Deck 21: Complex Numbers

Question 1

Write as an imaginary number: $\sqrt{-25}$

Answer 1

j5

Question 2

Write $\sqrt{-\frac{9}{16}}$ as a complex number.

Answer 2

$j \frac{3}{4}$

Question 3

Write as a complex number in rectangular form: $2+\sqrt{-9}$

Answer 3

$2+j 3$

Question 4

Write as a complex number in rectangular form: $\sqrt{-3}-3$

Question 5

Write as a complex number in rectangular form: $\sqrt{-\frac{16}{25}}+8$

Question 6

Combine and simplify: $(3+j 2)+(5-j 7)$

Question 7

Combine and simplify: $(2-j 8)-(-5-j 3)$

Question 8

Combine and simplify: $(3+j 4)-(8-j 6)$

Question 9

Combine and simplify: $(16+j 27)-(8-j 16)$

Question 10

Combine and simplify: $\left(\frac{2}{3}+j \frac{3}{2}\right)-\left(\frac{3}{2}+j \frac{2}{3}\right)$

Question 11

Combine and simplify: $\left(\frac{1}{3}-\frac{j}{2}\right)+\left(\frac{1}{6}-\frac{j}{4}\right)$

Question 12

Evaluate: $j^{26}$

Question 13

Evaluate: $j^{79}$

Question 14

Evaluate: $j^{2008}$

Question 15

Multiply and simplify: $\sqrt{-98} \times \sqrt{-32}$

Question 16

Multiply and simplify:
$\sqrt{-9}(4-\sqrt{-36})$

Question 17

Multiply and simplify: $j 3 \cdot(4-j 2)$

Question 18

Multiply and simplify: $(2+j 8)(3-j 6)$

Question 19

Multiply and simplify: $(6-j 4)(5+j 2)$

Question 20

Multiply and simplify:
$(5-\sqrt{-4})(\sqrt{-64}-8)$

Question 21

Multiply and simplify: $(4-9 j)^{2}$

Question 22

Write the conjugate of $-6-j 9$ .

Question 23

Write the complex conjugate of this complex number: $a+j b$

Question 24

Divide and simplify: $\frac{4+j 5}{-2+j}$

Question 25

Divide and simplify: (3 - j11) ÷ (5 + j6)

Question 26

Solve for $x$ to three significant digits: $x^{2}-2 x+5=0$

Question 27

Solve for $x$ to three significant digits: $x^{2}+x+40=0$

Question 28

Solve for $x$ to three significant digits: $5 x^{2}+7 x+4=0$

Question 29

Solve for $x$ to three significant digits: $5 x^{2}-3 x+1=0$

Question 30

Solve for $\mathrm{y}$ to three significant digits: $3.2 y^{2}-6.1 y+12.7=0$

Question 31

Solve for $x$ to three significant digits: $5 x^{2}=4 x-17$

Question 32

Factor $x^{2}+81$ into complex factors.

Question 33

Factor $2 x^{2}+18$ into complex factors.

Question 34

Divide and simplify: $\frac{4+\sqrt{-25}}{2-\sqrt{-16}}$

Question 35

Multiply and simplify: $(3+2 j)^{3}$

Question 36

Graph the complex number $7+j 9$ .

Question 37

Graph the complex number $1+j$ .

Question 38

Graph this complex number: $-4+j 7$

Question 39

Graph this complex number: 6 - j9

Question 40

Graph this complex number: $-4+\mathrm{j} 6$

Question 41

Graph this complex number: $-8-j 3$

Question 42

Write this complex number in polar and trigonometric form: $2+j 10$

Question 43

Write this complex number in polar and trigonometric form: $1+j 9$

Question 44

Write $10+j 2$ in polar and trigonometric form.

Question 45

Write $9+j 5$ in polar and trigonometric form.

Question 46

Write ${-11+j 17}$ in polar and trigonometric form.

Question 47

Write ${ }^{8-j 6}$ in polar and trigonometric form.

Question 48

Write ${-15-j 22}$ in polar and trigonometric form.

Question 49

Write $6\left(\cos 82^{\circ}+j \sin 82^{\circ}\right)$ in rectangular and polar form.

Question 50

Write in polar and in rectangular form: $4\left(\cos 121^{\circ}+j \sin 121^{\circ}\right)$

Question 51

Write in rectangular and trigonometric form: $4 / \underline{112^{\circ}}$

Question 52

Write in rectangular and trigonometric form: $8 /-50^{\circ}$ . Use three significant digits for rectangular.

Question 53

Write in rectangular form: $32 /\underline{240^{\circ}}$

Question 54

Multiply: $8\left(\cos 36^{\circ}+j \sin 36^{\circ}\right)$ by $2\left(\cos 63^{\circ}+j \sin 63^{\circ}\right)$

Question 55

Multiply: $5.32 / \underline{37.9^{\circ}}$ by $3.84 / \underline{80.2^{\circ}}$

Question 56

Divide: $12\left(\cos 22^{\circ}+j \sin 22^{\circ}\right)$ by $3\left(\cos 12^{\circ}+j \sin 12^{\circ}\right)$

Question 57

Divide: $50.4\left(\cos 232^{\circ}+j \sin 232^{\circ}\right)$ by $16.8\left(\cos 54^{\circ}+j \sin 54^{\circ}\right)$

Question 58

Divide: $28\left(\cos 65^{\circ}+j \sin 65^{\circ}\right) \div 7\left(\cos 150^{\circ}+j \sin 150^{\circ}\right)$

Question 59

Divide: $\frac{45 / \underline{132^{\circ}}}{9 / \underline{58^{\circ}}}$

Question 60

Evaluate: $\left[3\left(\cos 55^{\circ}+j \sin 55^{\circ}\right)\right]^{4}$

Question 61

Evaluate: $\left[3\left(\cos 25^{\circ}+j \sin 25^{\circ}\right)\right]^{3}$

Question 62

Evaluate: $\left(4 / \underline{112^{\circ}}\right)^{2}$

Question 63

Evaluate: $\left(5 / \underline{40^{\circ}}\right)^{3}$

Question 64

Evaluate: $\sqrt[3]{4 / \underline{114^{\circ}}}$

Question 65

Evaluate: $\sqrt{9 / 60^{\circ}}$

Question 66

Evaluate: $\sqrt{25+j 32}$

Question 67

Evaluate: $\sqrt[3]{5.5+j 3.5}$

Question 68

Evaluate: $\sqrt[4]{16 / \underline{56^{\circ}}}$

Question 69

Multiply: $\left(8.5 \angle 235^{\circ}\right)\left(12.4 \angle 190^{\circ}\right)$

Question 70

Evaluate: $\sqrt[5]{32 \angle 120^{\circ}}$

Question 71

Write $8-\mathrm{j} 6$ in polar form. Use three significant digits.

Question 72

Express $5+j 6$ in exponential form.

Question 73

Express $8\left(\cos 60^{\circ}+j \sin 60^{\circ}\right)$ in exponential form.

Question 74

Express this complex number in exponential form: $\frac{\pi}{3 / \underline{3}}$

Question 75

Express in rectangular, polar, and trigonometric form: $4 e^{\mathrm{j} 2}$

Question 76

Express in rectangular, polar, and trigonometric form: $2 e^{\mathrm{j} 4}$

Question 77

Express $7.5 e^{j 2.7}$ in rectangular form. Use three significant digits.

Question 78

Express $12 e^{j \frac{5 \pi}{4}}$ in rectangular form.

Question 79

Multiply: $\left(4.5 e^{j 1.3}\right)\left(8.2 e^{j 0.4}\right)$

Question 80

Multiply: $8 e^{\mathrm{j} 2.5}$ by $3 e^{\mathrm{j} 1.1}$