Let f be a continuous complex function defined in the complex plane.
Suppose there is an integer n and a nonzero complex number such that lim z^(-n)f(z)=c
Prove that f(z)=0 for at least one complex number z
(the suggested three steps of the proof are included in the attached document)
It is suggested that we use the index/winding number of a curve to prove this.
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