Describe the set of points in the complex plane that satisfy the given equation:

$\displaystyle |z-1|=1$

$\displaystyle |z|+|-1|=1\Rightarrow \sqrt{x^2+y^2}+1=1\Rightarrow \sqrt{x^2+y^2}=0$

$\displaystyle x^2+y^2=0$

The answer is supposed to be a circle centered at (1,0) with a radius of 1.

What am I doing wrong?