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: 65

Answer

$1+i$

Work Step by Step

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