Homework Statement
Find the residue at each pole of zsin(pi*z)/(4z^2 - 1)
Homework Equations
An isolated singular point z0 of f is a pole of order m if and only if f(z) can be written in the form:
f(z) = phi(z)/(z-z0)^m
where phi(z) is analytic and nonzero at z0. Moreover,
Res(z=z0) f(z)...
Homework Statement
Compute the integral from 0 to 2∏ of:
sin(i*ln(2e^(iθ)))*ie^(iθ)/(8e^(3iθ)-1) dθ
(Sorry for the mess, I don't know how to use latex)
Homework Equations
dθ=dz/iz
sinθ = (z - z^(-1))/2i
The Attempt at a Solution
So I tried to change it into a contour integral of a...
Hey guys, sorry for sending out so many questions so fast. I just discovered this site, and it looks great. Plus, I have my first complex analysis midterm tomorrow, so I'm pretty stressed (you'd think after 4 years of math/econ/computer science you'd get used to it but there's nothing like the...
Evaluate the integral of f over the contour C where:
f(z) = 1/[z*(z+1)*(z+2)] where C = {z(t) = t+1 | 0 <= t < infinity}
Over this contour, is f a real valued function? z(t) just maps t to the t+1, so it seems as if the contour is a real-valued continuous function, and f does not have any...
Evaluate the integral over the contour C when:
f(z) = 1/z and C = {z(t) = sin(t) + icos(t) | 0 <= t <= 2*pi}
I know f(z) = 1/r*e^(-it) = 1/r(cos(t) + isin(t)). But, when I try to take the contour integral by integrating f[z(t)]*z'(t), I get really messy formulas ((1/r*cos(sin(t))...