Corollary 1.2.13: Dividing complex numbers geometrically

If z = r1 cis(s) and w = r2 cis(t) in polar coordinates then
z/w = r1 / r2 cis(s - t)
Context Context

We have already shown that

if z = r cis(t) then = r cis(-t)

But then

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).

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Interactive Complex Analysis, ver. 1.0.0
(c) 2006-2007, Bert G. Wachsmuth
Page last modified: May 29, 2007