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

Published by Pearson

# Chapter 10 - Exponents and Radicals - 10.8 The Complex Numbers - 10.8 Exercise Set: 90

#### Answer

$i$

#### Work Step by Step

Using $i^2=-1$ and the laws of exponents, the given expression, $i^{17} ,$ is equivalent to \begin{array}{l}\require{cancel} i^{16}\cdot i \\\\= \left( i^2 \right)^{8}\cdot i \\\\= \left( -1 \right)^{8}\cdot i \\\\= 1\cdot i \\\\= i \end{array}

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