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: 20

Answer

$-12-9i$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given expression, $ 3i(-3+4i) ,$ 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} 3i(-3)+3i(4i) \\\\= -9i+12i^2 .\end{array} Since $i^2=-1,$ the expression above is equivalent to \begin{array}{l}\require{cancel} -9i+12(-1) \\\\= -9i-12 \\\\= -12-9i .\end{array}
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