When Did the Concept of Residue in Complex Analysis Emerge?

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Please anyone tell me about when, why and how did the concept of residue in complex analysis started?
 
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Jean-le-Rond d'Alambert and Augustine Cauchy (and some others) made extensive studies of wave propagation along with fundamental mathematical discoveries relating to limits, continuity and covergence. Cauchy's integral theorem was one product of their investigations.
 

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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