Intermediate Algebra (6th Edition)

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

Chapter 9 - Cumulative Review: 36d

Answer

$\frac{1}{i}$

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. $i^{-13}=\frac{1}{i^{13}}=\frac{1}{(i^{4})^{3}\times i^{1}}=\frac{1}{(i^{4})^{3}\times i^{1}}=\frac{1}{1^{3}\times i}=\frac{1}{i}$
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