I am having a hard time understanding the difference between poles and zeros, and simple poles versus removable poles. For instance, consider [tex]f(z)=\frac{z^2}{sin(z)} [/tex]. we can expand sine into a power series and pull out a z, so doesn't that remove the singularity at z=0? Also, I don't see why n*pi would not also be removable since it doesn't seem to be a problem in the series expansion (but according to my graded homework, 0 is a zero and n*pi is a simple pole)... Can someone help me out here?(adsbygoogle = window.adsbygoogle || []).push({});

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# Complex analysis- poles vs. Zeros, etc.

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