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Contour integral by CIF

  1. Sep 7, 2009 #1
    1. The problem statement, all variables and given/known data

    let t be the triangle with vertices at the points -3, 2i, and 3, oriented counterclockwise. compute


    [tex] \int \frac {z+1}{z^2 + 1} dz [/tex]



    2. Relevant equations

    [tex] f(z) = \frac {1}{2 \pi i} * \int \frac {f(z)}{z - z_o} dz [/tex]

    3. The attempt at a solution

    the integrand fails to be analytic at z^2 = +/- i , but only the point i is inside the triangle t so I rewrote the equation as:

    [tex] \int \frac {\frac {z+1}{z+i}}{z-i} dz [/tex]

    = [tex] 2 \pi i * f(i) [/tex]

    = [tex] 2 \pi i * \frac {i+1}{2i} [/tex]

    is this correct? thanks!
     
    Last edited: Sep 7, 2009
  2. jcsd
  3. Sep 7, 2009 #2
    Good job! It looks good to me, but be sure to simplify your answer. Also, there was just a small typo in the relevant equations as the f(z) to the left of the equals sign should be f(z0), but this was obviously just a typo.
     
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