Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 11 - Additional Topics - 11.4 - Complex Numbers - Problem Set 11.4: 49

Answer

$-9+40i$

Work Step by Step

We multiply each term of the first complex number with the second complex number and simplify: $(4+5i)^{2}$ =$(4+5i)(4+5i)$ =$4(4+5i)+5i(4+5i)$ =$16+20i+20i+25i^{2}$ =$16+40i+25(-1)$ [We substitute -1 in place of $i^{2}$ as $i^{2}=-1$] =$16-25+40i$ =$-9+40i$
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