Answer
$\color{blue}{-3-i\sqrt{6}}$
Work Step by Step
Simplify $\sqrt{-24}$ to obtain:
$=\sqrt{4(-1)(6)}
\\=\sqrt{2^2(-1)(6)}
\\=2\sqrt{-1)(6)}$
Since $\sqrt{-1} = i$, the expression above simplifies to:
$=2i\sqrt{6}$
Thus, the given expression is equivalent to:
$=\dfrac{-6-2i\sqrt{6}}{2}$
Divide each term of the numerator by the denominator to obtain:
$=\dfrac{-6}{2} - \dfrac{2i\sqrt{6}}{2}
\\=\color{blue}{-3-i\sqrt{6}}$
