Corollary 1.2.13: Dividing complex numbers geometrically
If z = r1 cis(s) and w = r2 cis(t) in polar coordinates thenz/w = r1 / r2 cis(s - t)
We have already shown that
if z = r cis(t) then = r cis(-t)
1/z = (1/z)(/) = /|z|2 = /r2 = r cis(-t)/r2 = 1/r cis(-t)
But now the result follows from our previous result about multiplication (detail, please).