Mapping a complex circle to its square

[torquerotates]

1. The problem statement, all variables and given/known data
graph |z-1|=1 and then graph z^2



2. Relevant equations
z=x+iy



3. The attempt at a solution

well, |z-1|=1 => |(x-1)+iy|=1,

squaring both sides. we get, (x-1)^2+y^2=1. This is a circle. But how am i supposed to get z^2 from this? I dont know what to do with the inequality since i cant algebrically isolate the z.

[Mark44]

I'm confused, too. Maybe you're supposed to take the z values on the circle and square them. If that's the case, what you'd be graphing is the set {(z, z^2): |z - 1| = 1}.

If I were you, I'd get clarification from my prof.