Precalculus (6th Edition)

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

Chapter 1 - Equations and Inequalities - Test - Page 181: 17

Answer

(a) $ -1$ (b) $ i$ (c) $ i$

Work Step by Step

Use the property $i^2=-1$, we have: (a) $i^{42}=(i^2)^{21}=(-1)^{21}=-1$ (b) $i^{-31}=i(i)^{-32}=i(i^2)^{-16}=i(-1)^{-16}=i$ (c) $\frac{1}{i^{19}}=i^{-19}=i(i)^{-20}=i(i^2)^{-10}=i(-1)^{-10}=i$
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