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 - Page 463: 84

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. $i^{15}=i^{12}\times i^{3}=(i^{4})^{3}\times -i=(1)^{3}\times -i=1\times -i=-i$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.