Answer
$\frac{13}{15}-\frac{2}{5}i$
Work Step by Step
$\frac{5+4i}{3+6i}$
=$\frac{5+4i}{3+6i}\times\frac{3-6i}{3-6i}$
=$\frac{5(3-6i)+4i(3-6i)}{3^{2}-(6i)^{2}}$
=$\frac{15-30i+12i-24i^{2}}{9-36i^{2}}$
=$\frac{15-18i-24(-1)}{9-36(-1)}$
=$\frac{39-18i}{45}$
=$\frac{3(13-6i)}{45}$
=$\frac{(13-6i)}{15}$
=$\frac{13}{15}-\frac{6i}{15}$
=$\frac{13}{15}-\frac{2}{5}i$
