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The complex function

  1. Nov 19, 2009 #1
    1. The problem statement, all variables and given/known data

    How would I prove that [tex]ln (z)[/tex] is analytic?


    2. Relevant equations

    ...



    3. The attempt at a solution

    I rewrote it as [tex]ln (z) = ln (r) + i\theta[/tex]. But, I'm not quite sure how to apply Cauchy-Riemman conditions here.
     
  2. jcsd
  3. Nov 19, 2009 #2
    [tex]\frac{\partial f}{\partial x} = \frac{\partial f}{\partial r}\frac{\partial r}{\partial x} + \frac{\partial f}{\partial \theta}\frac{\partial \theta}{\partial x}[/tex]

    if you want to use the polar coordinates. Remember also that CR-equation can be written as

    [tex] i \frac{\partial f}{\partial x} = \frac{\partial f}{\partial y}. [/tex]
     
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