Complex Analysis

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


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.


Homework Equations





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
 

Answers and Replies

  • #2
392
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Find a path C such that [tex]\int_C \frac1z\,dz\neq0[/tex]
 

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