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.