- #1
claralou_
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Homework Statement
For R > 0,
assume ΓR is a circle {z ∈ C : |z| = R} with anticlockwise direction.
For which R>0, does the the function f(z) = 1/sin^(2)(z) be continuous on ΓR
and evaluate ∫_{ΓR} dz/sin^(2)(z) for each R (the answer may be dependent on R).
Homework Equations
sinx= (e^(ix) - e^(-ix)) / 2i (possibly)
Resf(z)= lim (pole x f(z))
The Attempt at a Solution
used 1/e^(iz) = sin(x)
so found
1/sin^{2}x = 1 / (e^{2iz}
Began using the
closed integral over C of f(z)dz = Integral from -R to +R of f(x)dx + integral f(z) dz
Found that there was a pole at z = 1/2i and found the residue at that point to be 1/(2ie)