I am stuck on the following question:

Find the poles of z/(1-exp(z)) and determine their orders.

I have the poles as being all z*2*Pi*i*k with k an integer other than 0 as I am not sure what happens at 0.

How do I find the order though? It seems to me that writing the series expansion out does not help much.

Thanks for any and all help (my guess is that the order is 1)