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    Representative Integral/Complex Plane/Closed Loop Contour

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    Representative Integral/Complex Plane/Closed Loop Contour

    See attached file for full problem description.

    © BrainMass Inc. brainmass.com October 9, 2019, 6:51 pm ad1c9bdddf
    https://brainmass.com/physics/mathematical-physics/representative-integral-complex-plane-closed-loop-contour-99970

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    Solution Preview

    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