I am stuck on a problem which is given as an exercise in my book. I really would like to solve it primarily by myself, but unfortunately I don't "see" the solution intuitively and therefore I have no good starting point. The problem is the following: Show that if $f$ has an isolated pole singularity at $c$, every neighborhood of $c$ that lies in the domain of f contains all complex numbers $z$ with $|z|>r$ , for some $r$ dependent on the choice of neighborhood. A small hint would be appreciated. It will allow me to get some sleep.
Problem concerning pole singularity.
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complex-analysis