Complex Analysis: Theory and Applications · Problem 2.5.14

Analytic and Harmonic Functions — Howell & Matthews

Mathematics — Complex Analysis · riemann-sphere-stereographic-projection

Problem

Show that

z = x + iy

, when mapped onto the Riemann sphere, has coordinates

\left(\frac{x}{x^2+y^2+1},\ \frac{y}{x^2+y^2+1},\ \frac{x^2+y^2}{x^2+y^2+1}\right).