Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 1 - 1.5 - Complex Numbers - 1.5 Exercises - Page 119: 53



Work Step by Step

$(4-5i)^2=4^2-2(4)(5i)+(5i)^2=16-40i-25=-9-40i$ $\frac{3i}{(4-5i)^2}=\frac{3i}{-9-40i}=\frac{3i}{-9-40i}\frac{-9+40i}{-9+40i}=\frac{3i(-9+40i)}{(-9-40i)(-9+40i)}=\frac{-27i+120i^2}{81-1600i^2}=\frac{-27i-120}{81+1600}=-\frac{120}{1681}-\frac{27}{1681}i$
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