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.
Please see the attached file for the fully formatted problems.
Taylor Series Representations and Residues are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.