# How do you simplify (2i)/(3-4i)?

Apr 16, 2016

Multiply by the complex conjugate of the denominator
to get $\frac{- 8 + 6 i}{25}$

#### Explanation:

$\frac{2 i}{3 - 4 i}$
$\textcolor{w h i t e}{\text{XXX}} = \frac{2 i}{3 - 4 i} \times \frac{3 + 4 i}{3 + 4 i}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{6 i - 8}{9 + 16}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{- 8 + 6 i}{25}$