I just have no idea how to apply Poisson summation formula. Can someone give some help?

a) Let $\displaystyle \tau$ be fixed with $\displaystyle Im(\tau)>0$. Apply the Poisson summation formula to $\displaystyle f(z)=(\tau +z)^{-k}$ where $\displaystyle k \geq 2$ to obtain

$\displaystyle \sum_{n=-\infty}^{\infty} \frac {1}{(\tau+n)^k}= \frac{(-2\pi i)^k}{(k-1)!} \sum_{m=1}^{\infty} m^{k-1} e^{2 \pi im \tau}$

b) Does this formula still hold whenever $\displaystyle \tau$ is any complex number that is not an integer?