#### Answer

$-2+i$

#### Work Step by Step

Multiply the numerator and denominator by the conjugate of the complex imaginary number.
$\frac{(-3+4i)}{(2-i)}\times\frac{(2+i)}{(2+i)}$
Use foil to expand numerator; use the difference of two squares to expand the denominator.
$\frac{-6-3i+8i+4i^2}{4-i^2}$
Remember that $i^2=-1$.
$\frac{-6+5i-4}{4+1}$
Combine like terms in both numerator and denominator.
$\frac{-10+5i}{5}$
Divide each by 5.
$-2+i$