#### Answer

$-\frac{19}{25}-\frac{42i}{25}$

#### Work Step by Step

$\frac{2-9i}{4+3i}$
=$\frac{2-9i}{4+3i}\times\frac{4-3i}{4-3i}$
=$\frac{(2-9i)(4-3i)}{(4+3i)(4-3i)}$
=$\frac{2(4-3i)-9i(4-3i)}{4^{2}-(3i)^{2}}$
=$\frac{8-6i-36i+27i^{2}}{16-9i^{2}}$
=$\frac{8-42i+27(-1)}{16-9(-1)}$
=$\frac{-19-42i}{25}$
=$-\frac{19}{25}-\frac{42i}{25}$