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    Complex Analysis Residues at Poles

    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)...
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    Complex Analysis Integration with Sin and Cos

    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...
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    Converting complex power series into a function

    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...
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    Complex analysis integration

    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...
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    Integrate over complex contour

    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))...