Finding the Residue of an Expression with a Constant

[touqra]

How do you get the residue of this expression:

$$\frac{1}{(e^z - k)}$$ where k is a constant.

 

[Kummer]

How do you get the residue of this expression:

$$\frac{1}{(e^z - k)}$$ where k is a constant.

In what contour? And what is k? Note if k is zero then it becomes 1/e^z which is analytic. But if k!=0 then there is a singularity which depends on the contour.