Reciprocal

The reciprocal of a Real or Complex Number $z\not=0$ is its Multiplicative Inverse $1/z$. The reciprocal of a Complex Number $z=x+iy$ is given by

$${1\over x+iy}={x-iy\over x^2+y^2} = {x\over x^2+y^2}-{y\over x^2+y^2}i.$$