Answer
$6-3i\sqrt{3}$
Work Step by Step
Using $i=\sqrt{-1}$ and the properties of radicals, the given expression, $
(8-\sqrt{-3})-(2+\sqrt{-12})
,$ simplifies to
\begin{array}{l}\require{cancel}
8-\sqrt{-3}-2-\sqrt{-12}
\\\\=
(8-2)+(-\sqrt{-3}-\sqrt{-12})
\\\\=
(8-2)+(-\sqrt{-1}\cdot\sqrt{3}-\sqrt{-1}\cdot\sqrt{12})
\\\\=
(8-2)+(-i\sqrt{3}-i\cdot\sqrt{12})
\\\\=
(8-2)+(-i\sqrt{3}-i\cdot\sqrt{4\cdot3})
\\\\=
(8-2)+(-i\sqrt{3}-i\cdot\sqrt{(2)^2\cdot3})
\\\\=
(8-2)+(-i\sqrt{3}-i\cdot2\sqrt{3})
\\\\=
(8-2)+(-i\sqrt{3}-2i\sqrt{3})
\\\\=
6-3i\sqrt{3}
.\end{array}
