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    Zeroes of functions

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    Locate all zeros and singularities for each of the attached functions.

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    Answer b, c, d, and e.

    (b) Zero at z = n*pi, where n is any integer. Singularity at z = 0 (isolated)
    f(z) = .
    (c) Zero at z = 0, Singularity at z = n*pi, where n is any integer (isolated)
    f(z) = .

    (d) No zeros. Singularity at z = i, -i (isolated)
    f(z) = .

    (e) Zero at z = 0, Singularity at z = 0 (isolated)
    f(z) =

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    https://brainmass.com/math/graphs-and-functions/locate-all-zeros-singularities-25033

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    (b) We know and , then we have

    Thus is a pole and it is a removable singularity. The order is and the value of the function at this point is ...

    Solution Summary

    This shows how to locate all zeros and singularities for functions. The expert locates all zeros and singularities.

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