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 - 10.8 The Complex Numbers - 10.8 Exercise Set: 96

Answer

$i$

Work Step by Step

Using $i^2=-1$ and the laws of exponents, the given expression, $ 5i^5+4i^3 ,$ is equivalent to \begin{array}{l}\require{cancel} 5i^4\cdot i+4i^2\cdot i \\\\= 5(i^2)^2\cdot i+4i^2\cdot i \\\\= 5(-1)^2\cdot i+4(-1)\cdot i \\\\= 5(1)\cdot i+4(-1)\cdot i \\\\= 5i-4i \\\\= i \end{array}
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