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Homework Help: Complex analysis integration

  1. Sep 23, 2011 #1
    Evaluate the integral of f over the contour C where:

    f(z) = 1/[z*(z+1)*(z+2)] where C = {z(t) = t+1 | 0 <= t < infinity}

    Over this contour, is f a real valued function? z(t) just maps t to the t+1, so it seems as if the contour is a real-valued continuous function, and f does not have any explicit imaginary parts in it that are dependent on t. I was able to get f into partial fractions, but was a little confused about this.

    Any help would be greatly appreciated, as I have a midterm on this stuff tomorrow.

    Last edited: Sep 23, 2011
  2. jcsd
  3. Sep 23, 2011 #2


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    Science Advisor

    Yes, z is real. No, z is not "the next incremented real number"- there is no "next" number" in the real numbers. Since t goes from 0 to infinity, z goes from 1 to infinity. This integral is just the real integral
    [tex]\int_1^\infty \frac{dz}{z(z+1)(z+2)}[/tex]
    which can be done by "partial fractions". No complex numbers involved at all.
  4. Sep 23, 2011 #3
    Haha yeah, I definitely worded that incorrectly, just edited my original post. Thanks for the reply, that's exactly what I needed!
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