Perform the indicated operation. $\frac { 7 - 5 i } { 3 + 2 i }$
A) $- \frac { 11 } { 5 } - \frac { 29 } { 5 } i$
B) $7 - 5 i$
C) $- \frac { 11 } { 13 } - \frac { 29 } { 13 } i$
D) $\frac { 10 i ^ { 2 } - 29 i + 21 } { 3 + 2 i ^ { 2 } }$

Question

Quizplus · Accepted Answer

To divide complex numbers, you multiply the numerator and denominator by the conjugate of the denominator. The conjugate of $3 + 2i$ is $3 - 2i$. Multiplying both the numerator and denominator by this conjugate, we get: $\frac{(7 - 5i)(3 - 2i)}{(3 + 2i)(3 - 2i)}$. Simplifying this expression gives $\frac{21 - 14i - 15i + 10}{9 + 4}$, which simplifies further to $\frac{31 - 29i}{13}$, or $- \frac{11}{13} - \frac{29}{13}i$.

Perform the Indicated Operation 7−5i3+2i\frac { 7 - 5 i } { 3 + 2 i }3+2i7−5i​

Perform the Indicated Operation $\frac { 7 - 5 i } { 3 + 2 i }$