Perform the indicated operation. Write the result in the form a + bi.
-$\frac { 8 + 7 i } { 5 + 6 i }$
A) $- \frac { 2 } { 61 } - \frac { 83 } { 61 } \mathrm { i }$
B) $\frac { 82 } { 61 } - \frac { 13 } { 61 } \mathrm { i }$
C) $\frac { 2 } { 11 } + \frac { 13 } { 11 } \mathrm { i }$
D) $- \frac { 82 } { 11 } + \frac { 13 } { 11 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To divide complex numbers, you multiply the numerator and denominator by the conjugate of the denominator. The conjugate of $5 + 6i$ is $5 - 6i$. So, $\frac { 8 + 7 i } { 5 + 6 i }$ becomes $\frac { (8 + 7i) \cdot (5 - 6i) } { (5 + 6i) \cdot (5 - 6i) }$. Simplifying, the numerator becomes $40 - 48i + 35i + 42$ and the denominator becomes $25 + 36$, which simplifies to $82 - 13i$ over $61$, or $\frac { 82 } { 61 } - \frac { 13 } { 61 } \mathrm { i }$.

Perform the Indicated Operation 8+7i5+6i\frac { 8 + 7 i } { 5 + 6 i }5+6i8+7i​

Perform the Indicated Operation $\frac { 8 + 7 i } { 5 + 6 i }$