Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - 1.3 Complex Numbers - 1.3 Exercises: 43

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: $=\dfrac{10}{5} + \dfrac{10i\sqrt{2}}{5} \\=\color{blue}{2+2i\sqrt{2}}$
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