Pole (Complex Analysis)/Examples/z^2 + 1 over z

Examples of Poles in the context of Complex Analysis
Let $f$ be the complex function:
 * $\forall z \in \C \setminus \set 0: \map f z = \dfrac {z^2 + 1} z$

Then $f$ has:
 * a simple pole at $z = 0$.