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Math Help - Complex Analysis Question regarding mappings.

  1. #1
    Junior Member ginafara's Avatar
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    Complex Analysis Question regarding mappings.

    I am studying for an exam and I missed this problem on a homework. Can someone help me with it so that I can understand it before the exam?

    I tried an approx along the lines of Mx+b but I butchered the problem... TIA

    Problem:

    Find the linear transformation w=f(z) that satisfies the following...

    circle |x|=1 maps onto a circle |w - 3 + 2i| = 5 and f(-i) = 3 + 3i...

    Any help would be appreciated...
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  2. #2
    Senior Member
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    Anchorage, AK
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    Geometry

    Think about it geometrically: you're mapping the unit circle to the circle with center 3-2i and radius 5, with the condition f(-i)=3+3i. What does f(z)=Mz+b with complex M and Z mean geometrically? It means we scale by |M|, rotate by \arg{M}, and then translate by b. Does that help?

    --Kevin C.
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