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Homework Help: Integrating the Complex conjugate of z with respect to z

  1. May 19, 2009 #1
    Im doing a bit of contour integration, and a question came up with a term in it am unsure of how to do: in its simplest form it would be


    where z is a complex number and [tex]\bar{z}[/tex] is it's conjugate. Hmm i can't get the formatting to work out properly.. :S
    Last edited: May 19, 2009
  2. jcsd
  3. May 19, 2009 #2


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    If you are integrating over a circular contour of radius R then zz*=R^2, so z*=R^2/z. Otherwise you just have to take the contour and write it as z=(x(t)+iy(t)), so z*=(x(t)-iy(t)).
  4. May 19, 2009 #3
    Well now i feel kind of stupid... its line intergration, not contour integration :P the question reads:

    Evaluate the integral:

    [tex]\int[/tex]( [tex]\bar{z}[/tex] +1 ) dz

    Where L is the line segment from -i to 1+i.

    normally i would just integrate and sub in start and end point, but i have totaly drawn a blank on what to do with the conjugate in this case...
  5. May 19, 2009 #4


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    Just treat it as a complex line integral. You can only 'sub in' endpoints if the function you are integrating is analytic and has an antiderivative. (z*+1) doesn't. Parametrize L as a function of t and integrate dt. Like I said, if you have z=(x(t)+iy(t)) then z*=(x(t)-iy(t)).
  6. May 19, 2009 #5
  7. May 19, 2009 #6
    I think it's time i went to sleep... Yeh now that you mention the lack of anti-derivative i knew that. I think a good nights sleep will prepare me better for this exam than grinding my head into non-exsistant problems...

    sorry to waste your time with inane questions lol... Thanks for the prompt responces.
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