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: 64

Answer

$21+20i$

Work Step by Step

Using $(a+b)^2=a^2+2ab+b^2$, or the square of a binomial, the given expression, $ (-5-2i)^2 ,$ simplifies to \begin{array}{l}\require{cancel} (-5)^2+2(-5)(-2i)+(-2i)^2 \\\\= 25+20i+4i^2 \\\\= 25+20i+4(-1) \\\\= 25+20i-4 \\\\= 21+20i .\end{array}
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