Answer
$-i$
Work Step by Step
Using the facts that $i=\sqrt{-1}$, $i^2=-1$, $i^3=-i$, $i^4=1$, and $a^{b+c}=a^b\cdot a^c$, we have:
$$
i^{23}=i^{3+20}=i^3i^{20}=i^3(i^4)^5=i^3=-i
.$$
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Appendix A - Review - A.11 Complex Numbers - A.11 Assess Your Understanding - Page A94: 33
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