Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 4 - Quadratic Functions and Equations - Chapter Review - Page 272: 76

Answer

$21-25i$

Work Step by Step

Using $(a+b)(c+d)=ac+ad+bc+bd$ or the FOIL Method, the given expression, $ (1-9i)(3+2i) ,$ is equivalent to \begin{align*} & 1(3)+1(2i)-9i(3)-9i(2i) \\&= 3+2i-27i-18i^2 \\&= 3+2i-27i-18(-1) &\text{ (use $i^2=-1$)} \\&= 3+2i-27i+18 \\&= (3+18)+(2i-27i) &\text{ (combine like terms)} \\&= 21+(-25i) \\&= 21-25i .\end{align*} Hence, the given expression simplifies to $ 21-25i $.
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