Answer
$\frac{-13}{25}+\frac{41i}{25}$
Work Step by Step
$\frac{5+7i}{3-4i}$
=$\frac{5+7i}{3-4i}\times\frac{3+4i}{3+4i}$
=$\frac{(5+7i)(3+4i)}{(3+4i)(3-4i)}$
=$\frac{5(3+4i)+7i(3+4i)}{3^{2}-(4i)^{2}}$
=$\frac{15+20i+21i+28i^{2}}{9-16i^{2}}$
=$\frac{15+41i+28(-1)}{9-16(-1)}$
=$\frac{-13+41i}{25}$
=$\frac{-13}{25}+\frac{41i}{25}$
