# Which type of singularity does this complex function have at z = ∞?

I'm trying to classify the type of singularity at z = ∞ (the point at infinity) of the complex function:

click to see the equation

Up to now, I've just been able to prove that ∞ is not a pole. So I would like to prove that it is either an essential singularity or a removable singularity. Thank you for your suggestions!

• See what happens when you put $z=n \ge 2$ and then $z=in$ – Conrad Oct 23 '20 at 13:54

At , $$z=n$$ for each $$1\neq n\in\mathbb{N}$$ , $$f(z)$$ have zeros.
So, $$z=\infty$$ is a isolated essential singularity of $$f(z)$$.
• I don't understand what are you saying? And by the way, the given function is undefined at $z=\infty$. Also, one thing , a complex function is well defined at $\infty$ only if function is constant. – A learner Oct 23 '20 at 16:48