#### Answer

$\frac{32}{41}-\frac{40i}{41}$

#### Work Step by Step

$\frac{8}{4+5i}$
=$\frac{8}{4+5i}\times\frac{4-5i}{4-5i}$
=$\frac{8(4-5i)}{4^{2}-(5i)^{2}}$
=$\frac{32-40i}{16-25i^{2}}$
=$\frac{32-40i}{16-25(-1)}$
=$\frac{32-40i}{41}$
=$\frac{32}{41}-\frac{40i}{41}$