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: 65

Answer

$3-i$

Work Step by Step

Multiplying by the conjugate of the denominator, the given expression, $ \dfrac{10}{3+i} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{10}{3+i}\cdot\dfrac{3-i}{3-i} \\\\= \dfrac{10(3)+10(-i)}{9-i^2} \\\\= \dfrac{30-10i}{9-(-1)} \\\\= \dfrac{30-10i}{10} \\\\= \dfrac{10(3-i)}{10} \\\\= \dfrac{\cancel{10}(3-i)}{\cancel{10}} \\\\= 3-i .\end{array}
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