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 - Review Exercises: Chapter 10 - Page 694: 55



Work Step by Step

Using the product of the sum and difference of like terms which is given by $(a+b)(a-b)=a^2-b^2,$ the given expression is equivalent to \begin{array}{l}\require{cancel} (2+5i)(2-5i) \\\\= (2)^2-(5i)^2 \\\\= 4-25i^2 .\end{array} Using $i^2=-1,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 4-25i^2 \\\\= 4-25(-1) \\\\= 4+25 \\\\= 29 .\end{array}
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