# Residue of e^(az)/(1+e^z)^2 at I Pi

## Homework Statement

I need to find the residue of e^(az)/(1+e^z)^2 at I Pi. For some reason this is such much harder than I thought it was going to be. Mathematica is not even helping :(.

## Homework Equations

Cauchy's kth Integral formula.

## The Attempt at a Solution

I made an attempt at doing a u substitution of u=e^z, but I ended up with a residue of 0, which was not what I was expecting. All this lead me to believe that you probably can't use u-substitution strategies with line integrals and expect them to work.

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vela
Staff Emeritus
$$e^{az} = e^{a(z-i\pi+i\pi)} = e^{ia\pi}e^{a(z-i\pi)}$$