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