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: 45

Answer

$\color{blue}{-\frac{1}{8}+\frac{\sqrt2}{8}i}$

Work Step by Step

Simplify $\sqrt{-18}$ to obtain: $=\sqrt{9(-1)(2)} \\=\sqrt{3^2(-1)(2)} \\=3\sqrt{(-1)(2)}$ Since $\sqrt{-1} = i$, the expression above simplifies to: $=3i\sqrt{2}$ Thus, the given expression is equivalent to: $=\dfrac{-3+3i\sqrt{2}}{24}$ Divide each term of the numerator by the denominator to obtain: $=\dfrac{-3}{24} + \dfrac{3i\sqrt{2}}{24} \\=\color{blue}{-\frac{1}{8}+\frac{\sqrt2}{8}i}$
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