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I am asked to calculate the residues in the singular points of the function $f(z)=z^{100} \cos(1/z)$.

The problem is that I cannot find the singular points.

Any help will be much appreciated.

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    Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. Also, on this site we use MathJaX to format our maths. [Here](http://meta.math.stackexchange.com/q/5020/145141) you can find a basic tutorial. – 2017-01-04
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    I'll keep that in mind. Thank you! – 2017-01-05

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Let $w=1/z$. $\cos{w}$ is entire, so the only possible singularity in $\cos{(1/z)}$ is at $z=0$. Since $\cos{w}$ is not a polynomial, it has an essential singularity at $w=\infty$, so $\cos{(1/z)}$ has an essential singularity at $z=0$. Therefore you have to expand $ z^{100} \cos{(1/z)} $ in a power series to find the coefficient of $1/z$.