Answer
$\color{blue}{-\frac{1}{8}+\frac{\sqrt2}{8}i}$
Work Step by Step
Simplify $\sqrt{-18}$ to obtain:
$=\sqrt{9(-1)(2)}
\\=\sqrt{3^2(-1)(2)}
\\=3\sqrt{(-1)(2)}$
Since $\sqrt{-1} = i$, the expression above simplifies to:
$=3i\sqrt{2}$
Thus, the given expression is equivalent to:
$=\dfrac{-3+3i\sqrt{2}}{24}$
Divide each term of the numerator by the denominator to obtain:
$=\dfrac{-3}{24} + \dfrac{3i\sqrt{2}}{24}
\\=\color{blue}{-\frac{1}{8}+\frac{\sqrt2}{8}i}$
