Intermediate Algebra (6th Edition)

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

Chapter 7 - Section 7.7 - Complex Numbers - Exercise Set: 85

Answer

-i

Work Step by Step

Here, we are using the pattern of squaring i. For example, $i^{1}=i$, $i^{2}=-1$, $i^{3}=-1\times i=-i$, $i^{4}=-i\times i=-i^{2}=-1\times-1=1$, and so on. Therefore, we can use the fact that $i^{4}=1$ and then rewrite the expression in terms of $i^{4}$ in order to simplify. $i^{11}=i^{8}\times i^{3}=(i^{4})^{2}\times -i=(1)^{2}\times -i=1\times -i=-i$
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