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: 99



Work Step by Step

Apply exponent rule: $\displaystyle \quad a^{-n}=\frac{1}{a^{n}}$ $\displaystyle \frac{1}{i^{-11}}=\frac{1}{(\frac{1}{i^{11}})}=i^{11}$ $ i^{11}=i^{10+1}\qquad$...Apply exponent rule: $\quad a^{m+n}=a^{m}a^{n}$ $=i^{10}i\qquad$...Apply exponent rule: $\quad a^{mn}=(a^{m})^{n},\ i^{10}=(i^{2})^{5}$ $=i(i^{2})^{5}\qquad$...Apply imaginary number rule: $\quad i^{2}=-1$ $=(-1)^{5}i\qquad$...Apply exponent rule: $(-a)^{n}=-a^{n},$ if $n$ is odd $=-1^{5}i $=-1i$\qquad$...Multiply: $1i=i$ $=-i$
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