- #1
Physgeek64
- 247
- 11
Homework Statement
How would I calculate the residue of the function
##\frac{1}{(x^4+1)^2}##
Homework Equations
The Attempt at a Solution
So I have found that the poles are at
##z=e^{\frac{i \pi}{4}}##
##z=e^{\frac{3i \pi}{4}}##
##z=e^{\frac{5i \pi}{4}}##
##z=e^{\frac{7i \pi}{4}}##
I tried calculating this by finding its laurent series around each of the poles, but it was very algebraically heavy and I could not get the correct answer of
## \frac{3}{16 \sqrt{2}}+\frac{3}{16 \sqrt{2}}i##
I feel there must be an easier way. The standard residue formula also does not work here (i'm assuming because its a double pole)
Any help would be extremely appreciated!