Precalculus (6th Edition)

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

Chapter 1 - Equations and Inequalities - Quiz - Page 123: 6


$-\dfrac{1}{2} + \frac{\sqrt6}{4}i$

Work Step by Step

Divide 8 to each term of the numerator to obtain: $=\dfrac{-4}{8} + \dfrac{\sqrt{-24}}{8} \\=-\dfrac{1}{2} + \dfrac{\sqrt{4(-1)(6)}}{8} \\=-\dfrac{1}{2} + \dfrac{2\sqrt{-1(6)}}{8} \\=-\dfrac{1}{2}+\dfrac{\sqrt{-1(6)}}{4}$ Use the fact that $\sqrt{-1} = i$ to obtain: $=-\dfrac{1}{2}+\dfrac{i\sqrt{6}}{4} \\=-\dfrac{1}{2} + \frac{\sqrt6}{4}i$
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