Solution
= Solution
A squared <complex modulus> is nonnegative. Conversely, every nonnegative right-hand side of $|z+b|^2=|b|^2-c$ can be attained. The necessary and sufficient condition is therefore
$$
\boxed{c\leq |b|^2=b_1^2+b_2^2}.
$$
= Solution
A squared <complex modulus> is nonnegative. Conversely, every nonnegative right-hand side of $|z+b|^2=|b|^2-c$ can be attained. The necessary and sufficient condition is therefore
$$
\boxed{c\leq |b|^2=b_1^2+b_2^2}.
$$