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Math Help - Complex Analysis

  1. #1
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    Complex Analysis

    Determine, with motivation, all funtions that is analytic on
    {z/ |z| < 4}, with f( 0 ) = i and |f( z ) <= 1 on {z/ |z| < 4}
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  2. #2
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    Quote Originally Posted by JacquesRoux View Post
    Determine, with motivation, all funtions that is analytic on
    {z/ |z| < 4}, with f( 0 ) = i and |f( z ) <= 1 on {z/ |z| < 4}
    It seems your problem is faulty somehow. Because the way it is stated f(z) = i is the only such mapping. Because if f is non-constant then by the open mapping theorem f(0) has to be a mapped into an interior point of the range of f but that is not possible since f(0)=i is a boundary point. Thus, we conclude that constant functions are the only such functions, thus, f(z) = i for all |z|<4.
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    Thanks for your help!
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