Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Appendix A - Review - A.7 Complex Numbers; Quadratic Equations in the Complex Number System - A.7 Assess Your Understanding - Page A61: 47

Answer

$0$

Work Step by Step

Use the rule $a^{mn}=\left(a^m\right)^n$ to obtain: $i^6+i^4+i^2+1\\ =i^{2\cdot3}+i^{2\cdot2}+i^2+1\\ =(i^2)^3+(i^2)^2+i^2+1$ Use $i^2=-1$. $=(-1)^3+(-1)^2-1+1$ $=-1+1+0$ $=0$ Hence, the solution in the standard form is $0$.
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