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# Contour integral, residue theorem? Watch

1. I'm going over a past paper that has this question:

Evaluate

Where C is a circle in the complex plane with centre origin and radius 1.

So the only pole of is just z=0.

I'm guessing I should use the Cauchy residue theorem but I can't find the residue of at z=0.

Or is there another way of evaluating it?
2. HINT 1:

HINT 2:
3. (Original post by claret_n_blue)
HINT 1:

HINT 2:
doh! ok thanks a lot
4. (Original post by claret_n_blue)
HINT 1:

HINT 2:
Although this gives me 0 => residue of that pole =0 which I can't find by CRT =(
5. (Original post by jamie092)
Although this gives me 0 => residue of that pole =0 which I can't find by CRT =(
Show all of our working out that you've done so far
6. (Original post by jamie092)
Although this gives me 0 => residue of that pole =0 which I can't find by CRT =(
f(z) = 1/|z| isn't holomorphic (anywhere in , let alone around 0) so you cannot apply Cauchy's residue theorem.
7. Bigger hint:

Spoiler:
Show
What is |z| on the circle centered on the origin and radius 1?
8. I substituted e^it for z and ended up with e^i2pi - e^0 between 2pi and 0 which is 0.

Wait is that wrong? ;O
9. (Original post by Glutamic Acid)
f(z) = 1/|z| isn't holomorphic (anywhere in , let alone around 0) so you cannot apply Cauchy's residue theorem.
Doh!

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