I have been working on finding the isolated singularities of the following complex function:
$$\frac{3+z}{z^4(5+3z^2)}.$$
Clearly $0$ is a pole of order 4. But the written solution to the problem leaves the answer here. Surely we need to consider when $5+3z^2=0 \iff z = \pm \sqrt{ \frac{-5}{3}}$, but in the solutions there is no mention of this. Is there no singularity here?
Any help would be appreciated!