Answer
$-\frac{1}{8}+\frac{\sqrt{2}}{8}i$
Work Step by Step
Original Problem:
$\frac{-3 + \sqrt{-18}}{24}$
Factor out $\sqrt{-1}$ and 3 from $\sqrt{-18}$.
$\frac{-3+3\times\sqrt{-1}\times\sqrt{2}}{24}$
Recall that $\sqrt{-1}$ = $i$.
$\frac{-3+3i\sqrt{2}}{24}$
Simplify.
$\frac{-1+i\sqrt{2}}{8}$
Separate.
$-\frac{1}{8}+\frac{\sqrt{2}}{8}i$