Nobody seems to know the answer to this simple looking problem. I don't myself... Can YOU help ???
Consider in the complex plane two disks D1 and D2 defined by their respective centres C1 and C2 and radii R1 and R2. |C1|<=R1, |C2|>=R2. Let M1 be any point in the complex plane OUTSIDE D1 and let M2 be any point INSIDE D2.
Problem: Define in terms of C1, R1, C2 and R2 the locus of the product M1*M2.
Note: The solution is the whole complex plane minus a bounded domain containing the origin. The problem is thus to derive the equation (cartesian or polar) of the boundary of this locus.