Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 9 - Cumulative Review: 36c



Work Step by Step

In Section 7.7, we derived that $i^{4}=1$. Therefore, we can use this fact to write the equation in terms of $i^{4}$ and find the desired power of i. $i^{42}=i^{40}\times i^{2}=(i^{4})^{10}\times i^{2}=1^{10}\times -1=1\times -1=-1$ Here, we are using the fact that $i^{2}=-1$.
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