Divide and express the result in standard form.
-$\frac { 3 i } { 7 - 6 i }$
A) $- \frac { 18 } { 85 } + \frac { 21 } { 85 } \mathrm { i }$
B) $\frac { 21 } { 85 } - \frac { 18 } { 85 } \mathrm { i }$
C) $- \frac { 18 } { 13 } - \frac { 21 } { 13 } \mathrm { i }$
D) $\frac { 21 } { 13 } - \frac { 18 } { 13 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To divide complex numbers, you multiply the numerator and denominator by the conjugate of the denominator. The conjugate of $7 - 6i$ is $7 + 6i$. So, $\frac{3i}{7 - 6i} \cdot \frac{7 + 6i}{7 + 6i} = \frac{3i(7 + 6i)}{49 + 36} = \frac{21i + 18i^2}{85} = \frac{21i - 18}{85} = -\frac{18}{85} + \frac{21i}{85}$.

Divide and Express the Result in Standard Form 3i7−6i\frac { 3 i } { 7 - 6 i }7−6i3i​

Divide and Express the Result in Standard Form $\frac { 3 i } { 7 - 6 i }$