Pole (Complex Analysis)/Examples/Reciprocal of (z-3)^2 (z+1)

Examples of Poles in the context of Complex Analysis
Let $f$ be the complex function:
 * $\forall z \in \C \setminus \set {-1, 3}: \map f z = \dfrac 1 {\paren {z - 3}^2 \paren {z + 1} }$

Then $f$ has:
 * a pole of order $2$ at $z = 3$
 * a simple pole at $z = -1$.