I am confused about one particular problem regarding complex infinities. Suppose i have EXP[-z^2] with z being the complex number. Clearly it has poles at z=+i(infinity) and -i(infinity). . How to show that. If I replace w=1/Z then surely it doesn't work. So what should I do. Also I have a general question. When we talk about poles do we view all things in on Riemann surface .Then i(infinity) and-i (infinity) both correspond to the same pont (north pole). I am sorry for asking such sort of questions. but I am really not getting the point.