I need to find and classify the singularities of the function: $ f(z) = \frac{z^2+1} {z^4-2}$. I'm aware that I'm going to have to first find the Laurent series corresponding to this function. I have tried using partial fractions but haven't come to an answer. Any help is appreciated.
2026-03-24 23:52:28.1774396348
Finding the singularities of a complex function.
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That function has $4$ singularities, which are located at the $4$ fourth roots of $2$. Since the numerator doesn't vanish at any of them, $f$ has a simple pole at each one of them.