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Representative Integral/Complex Plane/Closed Loop Contour

Representative Integral/Complex Plane/Closed Loop Contour

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The results are ellipses centered on the origin.

To see it in detail, let us parametrize an original circle as z = r e^{i f} where
r and f are real, r=const > 0, and 0<=f<=2pi (that is the angle f is the parameter of the curve).

Then
Re(w1) = (r+1/r)*cos(f)
and
...

Solution Summary

The solution discusses the representative integral, the complex plane and a closed loop contour with required proofs.

$2.19