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Topic: MULTIPLICATION OF 2 DISKS IN COMPLEX PLANE ?
Replies: 1   Last Post: Jul 24, 1996 5:43 PM

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 Mr V. Besson Posts: 3 Registered: 12/12/04
MULTIPLICATION OF 2 DISKS IN COMPLEX PLANE ?
Posted: Jul 23, 1996 11:11 AM

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.

Any help would be most appreciated.
Vincent.

Date Subject Author
7/23/96 Mr V. Besson
7/24/96 Robert Israel