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: 46

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: $=\dfrac{-5}{10} + \dfrac{5i\sqrt{2}}{10} \\=\color{blue}{-\frac{1}{2}+\frac{\sqrt2}{2}i}$
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