Answer
$\displaystyle \frac{5}{13}+\frac{12}{13}i$
Work Step by Step
Recall, $i=\sqrt{-1}$, so $i^{2}=-1$. Thus, we multiply by the conjugate of the denominator to obtain:
$\displaystyle \frac{13}{5-12i}$
$\displaystyle =\frac{13}{5-12i}*\frac{5+12i}{5+12i}$
$\displaystyle=\frac{13(5+12i)}{(5-12i)(5+12i)}$
$\displaystyle =\frac{65+156i}{25+60i-60i-144i^{2}}$
$\displaystyle =\frac{65+156i}{25-144*-1}$
$\displaystyle=\frac{65+156i}{169}$
$\displaystyle =\frac{65}{169}+\frac{156}{169}i$
$\displaystyle =\frac{5}{13}+\frac{12}{13}i$
