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

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Some of the answers in the attachment are not correct. Here is my solutions.

(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 ...

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