# Chapter 1 - Equations and Inequalities - 1.3 Complex Numbers - 1.3 Exercises - Page 112: 44

$\color{blue}{10+i\sqrt{2}}$

#### 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: $=\dfrac{20}{2} + \dfrac{2i\sqrt{2}}{2} \\=\color{blue}{10+i\sqrt{2}}$

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