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Taylor Series Representation and Residue

Write f(z):=16z/(z^2 +1)^3

as f(z)= h(z)/(z - i)^3

with an explicit expression for the function h(z).

Explain why h(z) has a Taylor series representation about i and use this representation to find explicitly the principal part of
f at i. Hence, find the numerical value of the residue of f at i.

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