Divide.
-$\frac { 3 i } { 2 + 3 i }$
A) $\frac { 9 } { 13 } + \frac { 6 } { 13 } \mathrm { i }$
B) $- \frac { 6 } { 5 } - \frac { 9 } { 5 } i$
C) $\frac { 6 } { 13 } + \frac { 9 } { 13 } \mathrm { i }$
D) $- \frac { 9 } { 5 } + \frac { 6 } { 5 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To divide complex numbers, multiply the numerator and denominator by the complex conjugate of the denominator. The complex conjugate of $2 + 3i$ is $2 - 3i$. So,$$\frac { 3 i } { 2 + 3 i } = \frac { 3 i } { 2 + 3 i } \cdot \frac { 2 - 3 i } { 2 - 3 i } = \frac { 6 i - 9 i^2 } { 4 - 9 i^2 } = \frac { 6 i + 9 } { 13 } = \frac { 9 } { 13 } + \frac { 6 } { 13 } i$$

Divide - 3i2+3i\frac { 3 i } { 2 + 3 i }2+3i3i​

Divide
- $\frac { 3 i } { 2 + 3 i }$