Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - 1.3 Complex Numbers - 1.3 Exercises - Page 113: 98



Work Step by Step

Apply exponent rule: $\displaystyle \quad a^{-n}=\frac{1}{a^{n}}$ $i^{-14}=\displaystyle \frac{1}{i^{14}}$ Calculate $i^{14}$: $i^{14}=i^{2\cdot 7} \qquad$...Apply: $a^{mn}=(a^{m})^{n}$ $=(i^{2})^{7}\qquad$...Apply: $\quad i^{2}=-1$ $=(-1)^{7} \qquad$...Apply: $(-a)^{n}=-a^{n},$ if $n$ is odd. $=-1$
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