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: 84

Answer

$-\dfrac{1}{4}+\dfrac{5}{4}i$

Work Step by Step

Multiply both the numerator and the denominator by the conjugate of the denominator, which is $4i$, to obtain: $=\dfrac{(5+i)(4i)}{-4i(4i)} \\=\dfrac{20i+4i^2}{-16i^2}$ Use the fact that $i^2=-1$ to obtain: $=\dfrac{20i+4(-1)}{-16(-1)} \\=\dfrac{20i-4}{16} \\=\dfrac{-4+20i}{16} \\=-\dfrac{4}{16} + \dfrac{20}{16}i \\=-\dfrac{1}{4}+\dfrac{5}{4}i$
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