Solution
= Solution
The <triangle inequality> bounds the distance sum below by the separation of the two foci, which is two. Equality holds exactly for points on the closed segment joining them. Hence the <locus> is
$$
\boxed{x=0,\qquad0\le y\le2,\quad\text{equivalently }z=iy\ (0\le y\le2).}
$$
Both endpoints are included. It is the segment on the positive <imaginary axis> shown in the right-hand panel above.