Analyse convergence and absolute convergence of a complex series:
$$\sum_{n=1}^{\infty}\frac{e^{in}}{n^2}$$
Can I simply use a fact that $|e^z|=|e^xe^{iy}|=e^x$, so $\sum_{n=1}^{\infty}|\frac{e^{in}}{n^2}| = \sum_{n=1}^{\infty}\frac{1}{n^2}$ and so this series is absolutely convergent or do I have to use any other criterion?