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beefcake24
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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 function of z with the substitutions dθ=dz/iz and sinθ = (z - z^(-1))/2i. The dθ part is nice because we have ie^(iθ) in the equation so it cancels out. However, the sin function is not a function of theta but of a complex variable. I tried to reduce the inside of the sin as follows:
sin(i*ln(2e^iθ)) = sin(i*(ln2 + iθ)) = sin(i*ln2 - θ), but this doesn't really get me anywhere as the sin function is still not a function of theta.
Am I on the right track? And can anyone point me in the right direction of how to continue from here? Any help is much appreciated.
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