Complex Integral

[azure dome]

Can someone help me with this problem? I know that I need to represent sin(1/z) using taylor series, but after that, I do not know what to do. Thanks in advance!

[pastel phoenix]

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[civic shuttle]

Isnt the function f:z—>z^2sin(1/z) holomorphic on the circle C : |z|=1/2 ? If so why not apply Cauchy’s theorem

[stone crow]

is the curve positively oriented?

either way, I would apply residue theorem

[stone crow]

@azure dome

[azure dome]

No problem, I've managed the problem. Thanks for the help!

+close