Solution
= Solution
<Completing the square> directly with the <complex modulus> gives
$$
|z+b|^2=|b|^2-c.
$$
For $|b|^2>c$, this is the <circle> with <centre> $-b$ and <radius> $\sqrt{|b|^2-c}$. Equality gives just the point $-b$, and $|b|^2<c$ gives the empty <locus>. In particular, the nondegenerate answer is
$$
\boxed{\text{centre }-b,\qquad \text{radius }\sqrt{|b|^2-c}}.
$$