Answer
$16+30i$
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:
$=(-5-i\sqrt{9})^2
\\=(-5-i\sqrt{3^2})^2
\\=(-5-3i)^2$
Use rule (1) above with $a=-5$ and $b=3i$ to obtain:
$=(-5)^2-2(-5)(3i) + (3i)^2
\\=25+30i+9i^2$
Use rule (3) above to obtain:
$=25+30i+9(-1)
\\=25+30i-9
\\=16+30i$
