Answer
$-2\sqrt {6}+0i$.
Work Step by Step
The given expression is
$=\sqrt {-8}\cdot \sqrt {-3}$
$=\sqrt {2^2\cdot2\cdot (-1)}\cdot \sqrt {3\cdot (-1)}$
Use product rule.
$=2\sqrt {2}\cdot \sqrt {-1}\cdot \sqrt {3}\cdot \sqrt {-1}$
Use $\sqrt{-1}=i$
$=2\sqrt {2}\cdot i\cdot \sqrt {3}\cdot i$
Simplify
$=2\sqrt {2}\cdot \sqrt {3}\cdot i^2$
Use product rule and $i^2=-1$.
$=-2\sqrt {2\cdot 3}$
Simplify.
$=-2\sqrt {6}$.
Rewrite as $a+bi$.
$=-2\sqrt {6}+0i$.
