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: 54

Answer

$8+31i$

Work Step by Step

Using $(a+b)(c+d)=ac+ad+bc+bd$, or the product of 2 binomials, and the properties of radicals, the given expression, $ (-4+5i)(3-4i) ,$ simplifies to \begin{array}{l}\require{cancel} -4(3)-4(-4i)+5i(3)+5i(-4i) \\\\= -12+16i+15i-20i^2 \\\\= -12+31i-20i^2 \\\\= -12+31i-20(-1) \\\\= -12+31i+20 \\\\= 8+31i .\end{array}
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