Solution
= Solution
The <complex modulus> is a nonnegative <real number>. Equality therefore requires $z-1$ itself to be real and nonnegative. Its <imaginary part> gives $y=0$, and its <real part> then gives $x-1\geq0$. Conversely every such point satisfies the equality. Hence the complete <solution set> is
$$
\boxed{y=0,\qquad x\geq1}.
$$
Geometrically this is the closed ray on the <real axis> starting at $z=1$.