Conformal inversion of a quadrant
= Conformal inversion of a quadrant
{title2=$w=-1/z$}
The map $w=-1/z$ sends the open second quadrant inside the unit circle bijectively to the open first quadrant outside it. Radius becomes $r^{-1}$ and argument becomes $\pi-\theta$. Its derivative $1/z^2$ is nonzero on the source, so it is a <conformal map>. Rotation combined with reciprocal inversion similarly maps other quarter-disc regions.