Answer
$-8i$
Work Step by Step
RECALL:
(1) $(a+b)^2 = a^2+2ab+b^2$
(2) $\sqrt{-1}=i$
(3) $i^2=-1$
(4) For any real number $a \gt 0$, $\sqrt{-a} = i\sqrt{a}$.
Use rule (4) above to obtain:
$=(-2+i\sqrt{4})^2
\\=(-2+i\sqrt{2^2})^2
\\=(-2+2i)^2$
Use rule (1) above with $a=-2$ and $b=2i$ to obtain:
$=(-2)^2+2(-2)(2i) + (2i)^2
\\=4-8i+4i^2$
Use rule (3) above to obtain:
$=4-8i+4(-1)
\\=4-8i-4
\\=-8i$
