calculus - Test $x_n = (n+ipi)^n n^{-n + 1/n}$ for convergence and give its limit if possible.

Test $x_n = (n+i\pi)^n n^{-n + 1/n}$ for convergence and give its limit if possible.

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I'm not really sure what to do here. My first instinct was to rewrite the sequence as $x_n= (n+i\pi)^n n^{-n} n^{1/n}$ and evaluate the limits, but I'm left with $\lim_{n\rightarrow\infty} n^{1/n}=1$ and $\lim_{n\rightarrow\infty} n^{-n}=0$, which leaves me with nothing really. Can somebody help out?