Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Test: 30

Answer

$-\frac{3}{2}+\frac{5}{2}i$

Work Step by Step

$\frac{1+4i}{1-i}\times\frac{1+i}{1+i}$ =$\frac{(1+4i)(1+i)}{(1-i)(1+i)}$ =$\frac{1(1+i)+4i(1+i)}{(1)^{2}-(i)^{2}}$ =$\frac{1+i+4i+4i^{2}}{1-(-1)}$ =$\frac{1+5i+4(-1)}{2}$ =$\frac{1-4+5i}{2}$ =$\frac{-3+5i}{2}$ =$-\frac{3}{2}+\frac{5}{2}i$
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