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    Cauchy's formula

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    See Attachment for equation

    We know that sin z and cos z are analytic functions of z in the whole z-plane, what can we conclude about *(see attachment for equations)* in the first quadrant

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    a) Integral [ Sin z / {z^2 - pi^2} ]
    (|z| =4)

    = Integral [ Sin z / {(z+pi)*(z-pi)} ]
    (|z| =4)

    Two poles z = -pi and z=pi both within the circle |z|=4

    Therefore, Integral = 2*pi*i*{R1+R2}
    where R1 and r2 are the residues ...

    Solution Summary

    This shows how to work with analytic trigonometric functions and Cacuhy's formula. The equations with new quadrants are determined.