Answer
$\color{blue}{10+i\sqrt{2}}$
Work Step by Step
Simplify $\sqrt{-8}$ to obtain:
$=\sqrt{4(-1)(2)}
\\=\sqrt{2^2(-1)(2)}
\\=2\sqrt{(-1)(2)}$
Since $\sqrt{-1} = i$, the expression above simplifies to:
$=2i\sqrt{2}$
Thus, the given expression is equivalent to:
$=\dfrac{20+2i\sqrt{2}}{2}$
Divide each term of the numerator by the denominator to obtain:
$=\dfrac{20}{2} + \dfrac{2i\sqrt{2}}{2}
\\=\color{blue}{10+i\sqrt{2}}$
