Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - Study Summary - Practice Exercises: 24

Answer

$-i$

Work Step by Step

The given expression, $ i^{39} ,$ is equivalent to \begin{array}{l}\require{cancel} i^{38}\cdot i \\\\= (i^{2})^{19}\cdot i .\end{array} Using $i^2=-1,$ the expression above is equivalent to \begin{array}{l}\require{cancel} (-1)^{19}\cdot i \\\\= (-1)\cdot i \\\\= -i .\end{array}
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