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Complex Analysis Question

  1. Apr 12, 2009 #1
    1. The problem statement, all variables and given/known data
    Show that if the analytic function w= f(z) maps a domain D onto a portion of a line, then f must be constant throughout D.


    2. Relevant equations



    3. The attempt at a solution
    I just have one question, can I write w = u(x,y) (a+bi) since it maps to a portion of a line? Where a,b, and u(x,y) are reals. From there I have shown that the derivatives are 0.
     
  2. jcsd
  3. Apr 12, 2009 #2
    Open mapping theorem!!!
     
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