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: 41

Answer

$\color{blue}{-3-i\sqrt{6}}$

Work Step by Step

Simplify $\sqrt{-24}$ to obtain: $=\sqrt{4(-1)(6)} \\=\sqrt{2^2(-1)(6)} \\=2\sqrt{-1)(6)}$ Since $\sqrt{-1} = i$, the expression above simplifies to: $=2i\sqrt{6}$ Thus, the given expression is equivalent to: $=\dfrac{-6-2i\sqrt{6}}{2}$ Divide each term of the numerator by the denominator to obtain: $=\dfrac{-6}{2} - \dfrac{2i\sqrt{6}}{2} \\=\color{blue}{-3-i\sqrt{6}}$
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