College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 1 - Section 1.3 - Complex Numbers; Quadratic Equations in the Complex Number System - 1.3 Assess Your Understanding: 19

Answer

$6+4i$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given expression, $ 2i(2-3i) ,$ use the Distributive Property and the equivalence $i^2=-1.$ $\bf{\text{Solution Details:}}$ Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 2i(2)+2i(-3i) \\\\= 4i-6i^2 .\end{array} Since $i^2=-1,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 4i-6(-1) \\\\= 4i+6 \\\\= 6+4i .\end{array}
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