Pole (Complex Analysis)/Examples/sin z over (z-pi) (z-2)^4

Examples of Poles in the context of Complex Analysis
Let $f$ be the complex function:
 * $\forall z \in \C \setminus \set 2: \map f z = \dfrac {\sin z} {\paren {z - \pi} \paren {z - 2}^4}$

Then $f$ has a pole of order $4$ at $z = 2$

Note that at $z = \pi$ there is no pole as the numerator is $0$ at that point.