Finding the Residue of an Expression with a Constant

touqra
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How do you get the residue of this expression:

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

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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