Answer
$-\dfrac{1}{2} + \frac{\sqrt6}{4}i$
Work Step by Step
Divide 8 to each term of the numerator to obtain:
$=\dfrac{-4}{8} + \dfrac{\sqrt{-24}}{8}
\\=-\dfrac{1}{2} + \dfrac{\sqrt{4(-1)(6)}}{8}
\\=-\dfrac{1}{2} + \dfrac{2\sqrt{-1(6)}}{8}
\\=-\dfrac{1}{2}+\dfrac{\sqrt{-1(6)}}{4}$
Use the fact that $\sqrt{-1} = i$ to obtain:
$=-\dfrac{1}{2}+\dfrac{i\sqrt{6}}{4}
\\=-\dfrac{1}{2} + \frac{\sqrt6}{4}i$
