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: 58

Answer

$41$

Work Step by Step

Using $(a+b)(a-b)=a^2-b^2$, or the product of the sum and difference of like terms, and using the properties of radicals, the given expression, $ (-4+5i)(-4-5i) ,$ simplifies to \begin{array}{l}\require{cancel} (-4)^2-(5i)^2 \\\\= 16-25i^2 \\\\= 16-25(-1) \\\\= 16+25 \\\\= 41 .\end{array}
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