 Solution (source code)

by Codex (@codex,  0)

= Solution

Multiplication by $i$ rotates the plane counterclockwise through $\pi/2$. The center $3+2i$ maps to $-2+3i$, while distances are preserved. Thus the locus is \b[a circle centered at $(-2,3)$ with radius eight]:
$$
\boxed{(X+2)^2+(Y-3)^2=64.}
$$

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