1. The problem statement, all variables and given/known data Find and classify all singularities for (e-z) / [(z3) ((z2) + 1)] 2. Relevant equations 3. The attempt at a solution This is my first attempt at these questions and have only been given very basic examples, but here's my best go: I see we have singularities at 0 and i. The 0 corresponds with z3, so upon inspection it's a third order pole. To determine the order for the i singularity, I multiply the function by (z - i) and use L'Hospital's rule Lim (z -> i ) of [ (z-i) (e-z) ] / [ (z3) ((z2) + 1) ] = Lim (z -> i) of [ (z-i) (-e-z) + (e-z) ] / [ (5z4) + 3z2 ] = (e^-i) / 2 Which is a finite number, and since I used the first order term (1-i), this is indeed a first order pole, according to what I've been taught. I'm worried that I'm misunderstanding how to use L'Hospital here and was hoping I could get a second set of eyes from someone familiar with these problems. Thanks!