Answer
$\displaystyle \frac{6}{5}+\frac{8}{5}i$
Work Step by Step
Recall, $i=\sqrt{-1}$, so $i^{2}=-1$. Thus, we multiply by the conjugate of the denominator to obtain:
$\displaystyle \frac{10}{3-4i}$
$\displaystyle =\frac{10}{3-4i}*\frac{3+4i}{3+4i}$
$\displaystyle =\frac{10(3+4i)}{(3-4i)(3+4i)}$
$\displaystyle =\frac{30+40i}{9+12i-12i-16i^{2}}$
$\displaystyle =\frac{30+40i}{9-16*-1}$
$\displaystyle =\frac{30+40i}{25}$
$\displaystyle =\frac{30}{25}+\frac{40}{25}j$
$\displaystyle =\frac{6}{5}+\frac{8}{5}i$
