1. The problem statement, all variables and given/known data Given f(z) = (1/(z-a))(1/z^2 - 1/a^2) a is a fixed complex value If you define a function over the complex numbers by mapping z to f(z) when z is not equal to a, how should this function be defined at a s.t. it's continuous at point a? Explain. 2. Relevant equations A function will be continuous at a if lim(z->a) f(z) = f(a) 3. The attempt at a solution f(z) = -(z+a) / (z^2 a^2) lim(z->a) = -2/a^2 = f(a) I'm really not sure how to explain it or "justify it" as I'm supposed to beyond the 2 lines written above. I'm really not sure what else is needed... If a is an interior point of the domain (?) then can't continuity be shown using the delta/epsilon definition?