Divide.
-$\frac { 5 } { 1 - 3 i }$
A) $\frac { 1 } { 2 } + \frac { 3 } { 2 } \mathrm { i }$
B) $\frac { 1 } { 2 } - \frac { 3 } { 2 } \mathrm { i }$
C) $- \frac { 5 } { 8 } - \frac { 15 } { 8 } i$
D) $- \frac { 5 } { 8 } + \frac { 15 } { 8 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To divide complex numbers, you multiply the numerator and denominator by the complex conjugate of the denominator. The complex conjugate of $1 - 3i$ is $1 + 3i$. So, $\frac{5}{1 - 3i} \cdot \frac{1 + 3i}{1 + 3i} = \frac{5(1 + 3i)}{1^2 + (3i)^2} = \frac{5 + 15i}{1 - 9} = \frac{5 + 15i}{-8} = -\frac{5}{-8} - \frac{15i}{-8} = \frac{5}{8} + \frac{15}{8}i = \frac{1}{2} + \frac{3}{2}i$.

Divide - 51−3i\frac { 5 } { 1 - 3 i }1−3i5​

Divide
- $\frac { 5 } { 1 - 3 i }$