Perform the indicated operation. Write the answer in the form a + bi.
-$$\frac { - 8 + 3 i } { 5 + 7 i }$$
A) $- \frac { 19 } { 74 } - \frac { 71 } { 74 } i$
B) $- \frac { 19 } { 74 } + \frac { 71 } { 74 } i$
C) $- \frac { 8 } { 5 } - \frac { 3 } { 7 } i$
D) $- \frac { 8 } { 5 } + \frac { 3 } { 7 } i$

Question

Quizplus · Accepted Answer

To divide complex numbers, multiply the numerator and denominator by the complex conjugate of the denominator.$$\frac { - 8 + 3 i } { 5 + 7 i } = \frac { - 8 + 3 i } { 5 + 7 i } \cdot \frac { 5 - 7 i } { 5 - 7 i }$$$$= \frac { - 40 + 56 i - 15 i + 21 i^2 } { 25 - 49 i^2 }$$$$= \frac { - 40 + 41 i - 21 } { 74 }$$$$= - \frac { 19 } { 74 } + \frac { 71 } { 74 } i$$

Perform the Indicated Operation −8+3i5+7i\frac { - 8 + 3 i } { 5 + 7 i }5+7i−8+3i​

Perform the Indicated Operation $\frac { - 8 + 3 i } { 5 + 7 i }$