Answer
$6-6i$
Work Step by Step
Using $i=\sqrt{-1}$ and the properties of radicals, the given expression, $
(8-\sqrt{-4})-(2+\sqrt{-16})
,$ simplifies to
\begin{array}{l}\require{cancel}
8-\sqrt{-4}-2-\sqrt{-16}
\\\\=
(8-2)+(-\sqrt{-4}-\sqrt{-16})
\\\\=
(8-2)+(-\sqrt{-1}\cdot\sqrt{4}-\sqrt{-1}\cdot\sqrt{16})
\\\\=
(8-2)+(-i\cdot\sqrt{(2)^2}-i\cdot\sqrt{(4)^2})
\\\\=
(8-2)+(-i\cdot2-i\cdot4)
\\\\=
(8-2)+(-2i-4i)
\\\\=
6-6i
.\end{array}
