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: 74

Answer

$\dfrac{7-2i}{5}$

Work Step by Step

Multiplying the denominator by $i$, the given expression, $ \dfrac{2+7i}{5i} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{2+7i}{5i}\cdot\dfrac{i}{i} \\\\= \dfrac{2(i)+7i(i)}{5i^2} \\\\= \dfrac{2i+7i^2}{5i^2} \\\\= \dfrac{2i+7(-1)}{5(-1)} \\\\= \dfrac{2i-7}{-5} \\\\= -\dfrac{2i-7}{5} \\\\= \dfrac{7-2i}{5} .\end{array}
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