Answer
$\color{blue}{2+2i\sqrt{2}}$
Work Step by Step
Simplify $\sqrt{-200}$ to obtain:
$=\sqrt{100(-1)(2)}
\\=\sqrt{10^2(-1)(2)}
\\=10\sqrt{(-1)(2)}$
Since $\sqrt{-1} = i$, the expression above simplifies to:
$=10i\sqrt{2}$
Thus, the given expression is equivalent to:
$=\dfrac{10+10i\sqrt{2}}{5}$
Divide each term of the numerator by the denominator to obtain:
$=\dfrac{10}{5} + \dfrac{10i\sqrt{2}}{5}
\\=\color{blue}{2+2i\sqrt{2}}$