- #1
Dixanadu
- 254
- 2
Homework Statement
So guys..the title says it! I need to find the residue of cot(z) at z=0.
Homework Equations
For this situation, since the pole order is 1
[itex]Residue=\lim_{z \to z_{0}}(z-z_{0})f(z)[/itex]
The Attempt at a Solution
So here's what I am doing in steps:
First, the singularity is at z=0. So [itex]z_{0}=0[/itex].
Then I multiply both sides by [itex](z-z_{0})=z[/itex]...to get [itex](z-z_{0})f(z)=zcot(z)[/itex]
Now taking the limit of this is as z = 0 is [itex]0 \times \frac{cos(0)}{sin(0)}=0[/itex]...but this is wrong, the residue is 1...
I know its something stupid that I am doing but what is it? even if i expand sin and cos I still end up with 0...