Answer
$-8(12+5i)$
Work Step by Step
$(-2+\sqrt -100)^{2}$
Using $\sqrt -b = i\sqrt b$
$(-2+\sqrt -100)^{2} = (-2+i\sqrt 100)^{2}$
$=(-2+10i)^{2}$
Using $(a+b)^{2}=(a)^{2}+2(a)(b)+(b)^{2}$
$(-2+10i)^{2}=(-2)^{2}+2(-2)(10i)+(10i)^{2}$
$=4-40i+100i^{2}$
[Substituting $i^{2}=-1$]
$=4-40i+100(-1)$
$=4-40i-100$
$=-40i-96$
$=-8(5i+12)$
In standard form,
$-8(12+5i)$