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.
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.