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: 72

Answer

$-i$

Work Step by Step

Multiply both the numerator and the denominator by the conjugate of the denominator, which is $1-i$, to obtain: $=\dfrac{(1-i)(1-i)}{(1+i)(1-i)}$ Simplify using the rules $(a-b)(a+b)=a^2-b^2$ and $(a-b)(a-b)=a^2-2ab+b^2$ to obtain: $=\dfrac{1^2-2(1)(i) + i^2}{1^2-i^2} \\=\dfrac{1-2i+i^2}{1-i^2}$ Use the fact that $i^2=-1$ to obtain: $=\dfrac{1-2i+(-1)}{1-(-1)} \\=\dfrac{-2i}{1+1} \\=\dfrac{-2i}{2} \\=-i$
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