Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.7 - Complex Numbers - Exercise Set - Page 570: 103

Answer

$-5+10i$.

Work Step by Step

The given expression is $=(2+i)^2-(3-i)^2$ Use the special formula $(A+B)^2=A^2+2AB+B^2$ We have $A=(2+i)$ and $B=(3-i)$. $=[(2+i)-(3-i)][(2+i)+(3-i)]$ Clear the parentheses. $=[2+i-3+i][2+i+3-i]$ Add like terms. $=[-1+2i][5]$ Use the distributive property. $=-5+10i$.
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