PDA

View Full Version : show z^2 maps the circle |z-1|=1 to a cardioid


oab729
Apr11-09, 09:03 PM
1. The problem statement, all variables and given/known data
show z^2 maps the circle |z-1|=1 to a cardioid 2(1+cos(theta))e^(i*theta)


2. Relevant equations



3. The attempt at a solution
I tried using the restriction |z-1| = 1 and simply got that r^2=2x.

Then I tried to apply that and got

z^2=2xe^(2i*theta)

I've been trying for a good 15 minutes.

oab729
Apr11-09, 09:07 PM
NVM, take z = 1+cos +isin