Answer
$(-2+\sqrt{-11})^{2}=-7-4\sqrt{11}i$
Work Step by Step
$(-2+\sqrt{-11})^{2}$
Evaluate the power:
$(-2+\sqrt{-11})^{2}=(-2)^{2}+(2)(-2)(\sqrt{-11})+(\sqrt{-11})^{2}=...$
$...=4-4\sqrt{-11}-11=-7-4\sqrt{-11}=...$
Rewrite $\sqrt{-11}$ as $(\sqrt{-1})(\sqrt{11})$:
$...=-7-4(\sqrt{-1})(\sqrt{11})=...$
Substitute $\sqrt{-1}$ by $i$ and simplify:
$...=-7-4\sqrt{11}i$
