In complex analysis, functions are studied that are differentiable (in the complex space) at almost all points. Zeroes and poles are very important concept.

**Zeros** are termed as points at which a function $f,f(z)=0$.

A **Pole** (also called an *isolated singularity*) is a point where the limit of a complex function inflates dramatically with polynomial growth.

More specifically, a point $z_{0}$ is a pole of a complex valued function f if the function value $f(z)$ tends to infinity as $z$ gets closer to $z_{0}$. If the limit is finite, then $z_{0}$ is not a pole.

$z_{0}$ is a pole of order $n$ if:

$z→z_{0}lim (z−z_{0})⋅f(z)=0$

What is done here is $f(z)$ is multiplied by $(z−z_{0})_{n}$ and then taking limit as $z$ approaches $z_{0}$. If the result is not equal to $0$, then $z_{0}$ is a pole.