Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Appendix G - Complex Numbers - G Exercises: 9

Answer

$=\frac{1}{2}-\frac{1}{2}i$

Work Step by Step

$\displaystyle \frac{1}{1+i}$ We multiply the numerator and denominator by the conjugate of the denominator: $=\frac{1}{1+i}\cdot\frac{1-i}{1-i}$ We use the fact that $i^2=-1$ (because $i=\sqrt{-1}$) $=\frac{1-i}{1--1}$ $=\frac{1-i}{2}$ $=\frac{1}{2}-\frac{1}{2}i$
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