## Precalculus: Mathematics for Calculus, 7th Edition

$\dfrac{1}{1+i}=\dfrac{1}{2}-\dfrac{1}{2}i$
$\dfrac{1}{1+i}$ Multiply the fraction by $\dfrac{1-i}{1-i}$ $\Big(\dfrac{1}{1+i}\Big)\Big(\dfrac{1-i}{1-i}\Big)=\dfrac{1-i}{1-i^{2}}=...$ Since $i^{2}=-1$, the equation becomes: $...=\dfrac{1-i}{1-(-1)}=\dfrac{1-i}{2}=\dfrac{1}{2}-\dfrac{1}{2}i$