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Math Help - Complex open mapping & conformal mapping problems.

  1. #1
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    Complex open mapping & conformal mapping problems.

    1. Let f(0,2) -> C be a holomorphic function. Suppose that f is real-valued
    on the set {|z| = 1}. Show that f is a constant.
    2. Can you find a 1-1 conformal map from {z complex number | 0 < |z| < 1}
    onto the annulus X = {z complex | 1 < |z| < 2}.

    Thanks for helping.
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  2. #2
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    Domain of a function in 1. is a disc centered at 0 and radius 2. ^^'
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