Residue at $z=0$ for the complex function $8z^2\sin(\frac{1}{z})$

Asked Oct 23 '20 at 14:06

Active Oct 23 '20 at 14:16

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I'm just learning calculating residue please help.

edited Oct 23 '20 at 14:16

Alessio K

10,599

asked Oct 23 '20 at 14:06

Eemeli Häyrynen

1

Does the 8 have any impact on the answer? – Eemeli Häyrynen Oct 23 '20 at 14:32
Yes, it gets multiplied by $8$. So for your case we have $\text{Res}(f,0)=-\frac{8}{6}=-\frac{4}{3}.$ – Alessio K Oct 23 '20 at 14:34
thank you so much – Eemeli Häyrynen Oct 23 '20 at 14:35
You're welcome! :-) – Alessio K Oct 23 '20 at 14:35

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