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 - Study Summary - Practice Exercises: 22

Answer

$-32-26i$

Work Step by Step

Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ then \begin{array}{l}\require{cancel} (1-7i)(3-5i) \\\\= 1(3)+1(-5i)-7i(3)-7i(-5i) \\\\= 3-5i-21i+35i^2 .\end{array} Using $i^2=-1$ and then combining like terms, the expression above is equivalent to \begin{array}{l}\require{cancel} 3-5i-21i+35i^2 \\\\= 3-5i-21i+35(-1) \\\\= 3-5i-21i-35 \\\\= (3-35)+(-5i-21i) \\\\= -32-26i .\end{array}
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