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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!

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    It's not clear to me what you want. Yes, the function has simple poles at $\pm i\sqrt{5/3}$ too. Is your question whether that is right, or why these haven't been mentioned in the solution? – 2017-02-26
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    You edited to make it clear just before I posted my comment. You're right, and one could only guess why the solution doesn't mention these poles. – 2017-02-26

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