Convergent Complex Series/Examples/((2+3i) over (4+i))^n

Example of Convergent Complex Series
The series $\displaystyle \sum_{n \mathop = 1}^\infty a_n$, where:
 * $a_n = \paren {\dfrac {2 + 3 i} {4 + i} }^n$

is convergent.

Proof
Thus $\displaystyle \sum_{n \mathop = 1}^\infty \paren {\dfrac {2 + 3 i} {4 + i} }^n$ is absolutely convergent by Sum of Infinite Geometric Sequence.

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