#### Answer

$10+i\sqrt{2}$

#### Work Step by Step

Original Problem:
$\frac{20 + \sqrt{-8}}{2}$
Factor out $\sqrt{-1}$ and 2 from $\sqrt{-8}$.
$\frac{20+\sqrt{-1}\times2\sqrt{2}}{2}$
Recall that $\sqrt{-1}$ = $i$.
$\frac{20+2i\sqrt{2}}{2}$
Divide each numerator term by 2.
$10+i\sqrt{2}$