Answer
$\color{blue}{-\frac{1}{2}+\frac{\sqrt2}{2}i}$
Work Step by Step
Simplify $\sqrt{-50}$ to obtain:
$=\sqrt{25(-1)(2)}
\\=\sqrt{5^2(-1)(2)}
\\=5\sqrt{(-1)(2)}$
Since $\sqrt{-1} = i$, the expression above simplifies to:
$=5i\sqrt{2}$
Thus, the given expression is equivalent to:
$=\dfrac{-5+5i\sqrt{2}}{10}$
Divide each term of the numerator by the denominator to obtain:
$=\dfrac{-5}{10} + \dfrac{5i\sqrt{2}}{10}
\\=\color{blue}{-\frac{1}{2}+\frac{\sqrt2}{2}i}$
