Find the quotient. Write the answer in standard form.
-$$\frac { 9 + 2 i } { 4 + 9 i }$$
A) $\frac { 18 } { 97 } - \frac { 89 } { 97 } \mathrm { i }$

B) $\frac { 54 } { 97 } - \frac { 73 } { 97 } \mathrm { i }$

C) $- \frac { 18 } { 65 } - \frac { 73 } { 65 } \mathrm { i }$

D) $- \frac { 54 } { 65 } - \frac { 73 } { 65 } \mathrm { i }$

Question

Find the quotient. Write the answer in standard form.
-$$\frac { 9 + 2 i } { 4 + 9 i }$$
A) $\frac { 18 } { 97 } - \frac { 89 } { 97 } \mathrm { i }$

B) $\frac { 54 } { 97 } - \frac { 73 } { 97 } \mathrm { i }$

C) $- \frac { 18 } { 65 } - \frac { 73 } { 65 } \mathrm { i }$

D) $- \frac { 54 } { 65 } - \frac { 73 } { 65 } \mathrm { i }$

Quizplus · Accepted Answer

To find the quotient of $\frac { 9 + 2 i } { 4 + 9 i }$, we multiply both the numerator and the denominator by the conjugate of the denominator, which is $4 - 9i$. This gives us $\frac{(9 + 2i)(4 - 9i)}{(4 + 9i)(4 - 9i)}$. Simplifying, we get $\frac{36 - 81i + 8i - 18i^2}{16 - 81i^2}$. Since $i^2 = -1$, this simplifies further to $\frac{36 + 18 + 8i - 81i}{16 + 81}$, which simplifies to $\frac{54 - 73i}{97}$. Therefore, the quotient in standard form is $\frac{54}{97} - \frac{73}{97}i$.

Find the Quotient 9+2i4+9i\frac { 9 + 2 i } { 4 + 9 i }4+9i9+2i​

Find the Quotient $\frac { 9 + 2 i } { 4 + 9 i }$