Complex Analysis: Evaluating an Integral over a Contour

[beefcake24]

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.

Thanks!

 

[HallsofIvy]

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
$$\int_1^\infty \frac{dz}{z(z+1)(z+2)}$$
which can be done by "partial fractions". No complex numbers involved at all.

 

[beefcake24]

Haha yeah, I definitely worded that incorrectly, just edited my original post. Thanks for the reply, that's exactly what I needed!