The **pole** of a meromorphic complex function is a point on the complex plane on which the function is undefined, or approaches infinity. Any rational complex function will have poles where the denominator is equal to zero. A function

will have a pole of order *n* when *z=p*. If *n = 1*, the point is called a **simple pole**. If *n = 0*, the point is a removable singularity (that is, the limit exists).