Complex Analysis Question

  • Thread starter oab729
  • Start date
  • #1
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Homework Statement


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.


Homework Equations





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.
 

Answers and Replies

  • #2
256
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Open mapping theorem!!!
 

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