## Intermediate Algebra (12th Edition)

Published by Pearson

# Chapter 7 - Section 7.7 - Complex Numbers - 7.7 Exercises - Page 491: 62

#### Answer

$53$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given expression, $(7+2i)(7-2i) ,$ use the special product on multiplying the sum and difference of like terms. Then use $i^2=-1.$ $\bf{\text{Solution Details:}}$ Using the product of the sum and difference of like terms which is given by $(a+b)(a-b)=a^2-b^2,$ the expression above is equivalent \begin{array}{l}\require{cancel} (7)^2-(2i)^2 \\\\= 49-4i^2 .\end{array} Since $i^2=-1,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 49-4(-1) \\\\= 49+4 \\\\= 53 .\end{array}

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