Divide Complex Numbers
Divide and express the result in standard form.
-$\frac { 4 i } { 2 - i }$
A) $- \frac { 4 } { 5 } + \frac { 8 } { 5 } i$
B) $\frac { 4 } { 5 } + \frac { 8 } { 5 } \mathrm { i }$
C) $- \frac { 4 } { 3 } + \frac { 8 } { 3 } \mathrm { i }$
D) $- \frac { 4 } { 5 } - \frac { 8 } { 5 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To divide complex numbers, you multiply the numerator and denominator by the conjugate of the denominator. The conjugate of $2 - i$ is $2 + i$. So, $\frac{4i}{2-i} \cdot \frac{2+i}{2+i} = \frac{4i(2+i)}{2^2 - (-1)} = \frac{8i + 4i^2}{5} = \frac{8i - 4}{5} = -\frac{4}{5} + \frac{8}{5}i$.

Divide Complex Numbers Divide and Express the Result in Standard 4i2−i\frac { 4 i } { 2 - i }2−i4i​

Divide Complex Numbers
Divide and Express the Result in Standard $\frac { 4 i } { 2 - i }$