Convergent Complex Series/Examples/1 over n^2 - i n

Example of Convergent Complex Series
The series $\displaystyle \sum_{n \mathop = 1}^\infty a_n$, where:
 * $a_n = \dfrac 1 {n^2 - i n}$

is convergent.

Proof
Thus $\displaystyle \sum_{n \mathop = 1}^\infty \dfrac 1 {n^2 - i n}$ is absolutely convergent.

The result follows from Absolutely Convergent Series is Convergent: Complex Numbers.