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: 54

Answer

$23+i$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given expression, $ (7-2i)(3+i) ,$ use the FOIL method. Then use $i^2=-1$ and combine like terms. $\bf{\text{Solution Details:}}$ Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the expression above is equivalent to\begin{array}{l}\require{cancel} 7(3)+7(i)-2i(3)-2i(i) \\\\= 21+7i-6i-2i^2 .\end{array} Since $i^2=-1,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 21+7i-6i-2(-1) \\\\= 21+7i-6i+2 .\end{array} Combining like terms results to \begin{array}{l}\require{cancel} (21+2)+(7i-6i) \\\\= 23+i .\end{array}
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