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Polar Coordinates to evaluate integrals

  1. Mar 28, 2012 #1
    1. The problem statement, all variables and given/known data
    Use Polar coordinates to evaluate 2eydkky.png were C denotes the unit circle about a fixed point Z0 in the complex plane



    3. The attempt at a solution
    I've only used polar integrals to convert an integral in sin and cos into one in therms of z, find the residues and then use the residue theorum to evaluate the integral so I am not really sure where to go with this question? Any help would be greatly appreciated!
     
  2. jcsd
  3. Mar 28, 2012 #2

    HallsofIvy

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    Let [itex]z= z_0+ e^{i\theta}[/itex].
     
  4. Mar 28, 2012 #3
    Have I done it correctly if I end up with a final answer of
    2∏i(aZ02 + bZ0 + c)
    Thanks!
     
  5. Mar 28, 2012 #4

    HallsofIvy

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    Yes, in fact there is the "Cauchy integral formula" that says
    [tex]\oint \frac{f(z)}{z-z_0} dz= 2\pi if(z_0)[/tex]

    Perhaps this problem was intended as an introduction to that.
     
  6. Mar 28, 2012 #5
    Ah yes we have done that previously, I think I just need to do practise questions to bring all the theory together. Cheers
     
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