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Complex Analysis

  1. Apr 16, 2009 #1
    1. The problem statement, all variables and given/known data
    Prove that there does not exist an analytic function on the annulus D: 1<|z|<2, s.t. F'(z) = 1/z for all z in D.


    2. Relevant equations



    3. The attempt at a solution
    Assume F exists, then for z in D, not a negative number, F(z) = Log z + c since Log' z = 1/z... Lost
     
  2. jcsd
  3. Apr 17, 2009 #2
    Find a path C such that [tex]\int_C \frac1z\,dz\neq0[/tex]
     
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