Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Section 10.7 - Complex Numbers - Practice: 18

Answer

$-i$

Work Step by Step

$i^{11}=i^{8}\times i^{3}=(i^{2})^{4}\times i^{3}$ As $i^{3}=-i$ and $i^{2}=-1$, $(i^{2})^{4}\times i^{3}=(-1)^{4}\times(-i)=1\times-i=-i$. Therefore, $i^{11}=-i$.
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