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    (z,r) is a circular contour of radius r>0 centred at z

    Explain why.

    cannot be evaluated by applying Cauchy's integral formula with
    , when = 1. Hence evaluate the integral.

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    Solution Preview

    Observe that the function f(x, y) = (x, 0) is differentiable as a real-valued function,
    but not differentiable when viewed as a complex function, i.e. f(z) = Re(z)
    is not analytic (as neither is the ...

    Solution Summary

    The solution explains why a given integral cannot be evaluated using Cauchy's formula and how to evaluate the integral.