[Complex Analysis] Find the Residue at z=0 for z*cos(1/z)

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This short video introduces how to Find the Residue at z=0 for the function f(z)=z*cos(1/z).
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Can this question also be done using the 1/z^2 f(1/z) formula ?
im getting -1/2 as well using this

theneoncuber