1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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]
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook