Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 7 - Section 7.7 - Complex Numbers - 7.7 Exercises: 78

Answer

$5i-1$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To divide the given expression, $ \dfrac{5+i}{-i} ,$ multiply both the numerator and the denominator by $i$. Use $i^2=-1.$ $\bf{\text{Solution Details:}}$ Multiplying both the numerator and the denominator by $i,$ the expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{5+i}{-i}\cdot\dfrac{i}{i} \\\\= \dfrac{(5+i)i}{-i^2} .\end{array} Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{(5)i+(i)i}{-i^2} \\\\= \dfrac{5i+i^2}{-i^2} .\end{array} Since $i^2=-1,$ the expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{5i+(-1)}{-(-1)} \\\\= \dfrac{5i-1}{1} \\\\= 5i-1 .\end{array}
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