Evaluate the following integrals:
(a) integral over gamma of (e^z - e^-z)/(z^n) dz, where n is positive integer
and gamma(t) = e^(it), 0 =< t =< 2 pi
(b) integral over gamma of (dz/(z^2 + 1) ) where gamma(t) = 2e^(it),
0 =< t =< 2pi
( Hint: expand (z^2 + 1)^-1 by means of partial fractions
PLEASE USE POWER SERIES REPRESENTATION OF ANALYTIC FUNCTIONS, I only
want the answer to be done using power series representation of analytic functions.
This shows how to perform complex integration using power series representation.