Answer
$6-3i\sqrt 3$
Work Step by Step
$(8-\sqrt {-3})-(2+\sqrt {-12})$
=$(8-\sqrt {-1\times3})-(2+\sqrt {-1\times12})$
=$(8-\sqrt {-1}\sqrt 3)-(2+\sqrt {-1}\sqrt {12})$
=$(8-i\sqrt 3)-(2+i\sqrt {12})$
=$8-i\sqrt 3-2-i\sqrt {12}$
=$8-i\sqrt 3-2-i\sqrt {4\times3}$
=$8-i\sqrt 3-2-i\sqrt 4\sqrt 3$
=$8-2-i\sqrt 3-2i\sqrt 3$
=$6-3i\sqrt 3$