## Calculus 8th Edition

Published by Cengage

# Appendix G - Complex Numbers - G Exercises - Page A55: 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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