Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.7 - Complex Numbers - Exercise Set: 15

Answer

$-2 - 3i\sqrt{2}$

Work Step by Step

Factor the radicand so that one factor $-1$ to obtain: $=-2-\sqrt{18(-1)} \\=-2-\sqrt{2(9)(-1)} \\=-2-\sqrt{2(3^2)(-1)}$ RECALL: (1) $\sqrt{abc} = \sqrt{a} \cdot \sqrt{b} \cdot \sqrt{c}$ (2) $\sqrt{-1} = i$ Use rule (1) above to obtain: $=-2 - \sqrt{2} \cdot \sqrt{3^2} \cdot \sqrt{-1} \\=-2 - \sqrt{2} \cdot 3 \cdot \sqrt{-1} \\= -2 - 3\sqrt{2} \cdot \sqrt{-1}$ Use rule (2) above to obtain: $=-2 - 3\sqrt{2} \cdot i \\=-2 - 3i\sqrt{2}$
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