let $z_0 \in \mathbb{C}$ be a pole (non-essential singularity) of order $k$ of the complex function $g(z)$. Is $z_0$ an isolated singularity of $ \frac{1}{g(z)}$? If yes which type of singularity?
From my book "Conway's Functions of One Complex variable" the following is taken: Note that if $f$ has a pole at $a$, then $\frac{1}{f(z)}$ has a removable singularity there and extends to $a$ with value $0$."
So we know $z_0$ is a removable singularity of $\frac{1}{g(z)}$. How can I show/prove this statement?