Convergence of x_n: Limit in Complex Field

[BSCowboy]

Could someone please provide me a little direction.
I'm trying to show this sequence converges

x_n=n\left(e^{\frac{2\pi i}{n}}-1\right)

I know \lim_{n\rightarrow\infty}|x_n|=2\pi i, but I have no idea how to arrive at the solution.

This is not a homework question.

 

[nicksauce]

The obvious thing to do would be to expand the exponential term as a power series.