- #1
strangequark
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Homework Statement
Let [tex] \gamma_{r} [/tex] be the circle centered at 2i with a radius r. Compute:
[tex]\oint \frac{f(z)}{z^{2}+1}dz [/tex]
Homework Equations
[tex]2 \pi i f(w)=\oint \frac{f(z)}{z-w}dz[/tex]
Cauchy's integral formula... maybe?
The Attempt at a Solution
I can see how to find solutions for two separate cases:
0<r<1
0<r<3
r>3
I have no idea how to find a general formula for this... nor am I sure what to do when [tex]\gamma[/tex] passes thru a singularity...
any help on how to get started would be MUCH appreciated... thanks in advance