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Math Forum » Discussions » sci.math.* » sci.math.independent

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
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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.

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