1. The problem statement, all variables and given/known data Determine if the following are removable, pole (with order), or essential singularities. a) f(z) = (z^3+3z-2i)/(z^2+1) a=i b) f(z) = z/(e^z - 1) a=0 c) e^e^(-1/z) a=0 2. The attempt at a solution Part a is pretty straightforward, just simplify it down to (z-i)(z+2i)/(z+i) and the sing is removable with value 0. Part b is where I'm having some trouble. I'm pretty sure its also removable since when I graphed it the limit looks like it converges to 1. Though when I expand it out into a power series I cant seem to get it to work. z = Sigma (0 to inf over n) delta(n-1)z^n delta = Kroniker delta function, 1 at delta(0) and 0 everywhere else. e^z = Sigma (z^n/n!) -1 = -Sigma (d(n)z^n) After failing to come up with anything usefull with that method I decided to show that the actual limit was one. I couldnt seem to come up with a delta such that given an epsilon |z|<d => |f(z) - 1|<epsilon. Overall, I was wondering if you guys could give me some hints on how to tackle the problem.