Show z^2 maps the circle |z-1|=1 to a cardioid

[oab729]

Homework Statement

show z^2 maps the circle |z-1|=1 to a cardioid 2(1+cos(theta))e^(i*theta)

Homework Equations

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]

NVM, take z = 1+cos +isin