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## Main Question or Discussion Point

Hello!

I am studing for my Complex Analysis exam and solving the exercises for Residues given by the professor.

The problem is that for some exercises I get to a solution different from the one of the professor , and I am not sure that the mistake is in my calculations.

I would greatly appreciate it, if somebody could solve it and tell me what a solution he/she came up with.

Here is the exercise:

Calculate the residue of the complex-valued function [tex]f(z)[/tex] at [tex]z=-\imath[/tex], as:

My answer:

Thanks a lot!

I am studing for my Complex Analysis exam and solving the exercises for Residues given by the professor.

The problem is that for some exercises I get to a solution different from the one of the professor , and I am not sure that the mistake is in my calculations.

I would greatly appreciate it, if somebody could solve it and tell me what a solution he/she came up with.

Here is the exercise:

Calculate the residue of the complex-valued function [tex]f(z)[/tex] at [tex]z=-\imath[/tex], as:

[tex]f(z) = \frac{\sin(z)}{(z^2 + 1)^2}[/tex]

My answer:

[tex]Res(f(z),\imath) = -\frac{1}{4e}[/tex]

The professor's answer:[tex]Res(f(z),\imath) = \frac{\imath}{2}\cosh(1)[/tex]

Thanks a lot!

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