Having just gone through a section of complex analysis in a math course, I'm curious when you would actually use things like contour integration and residue theory in EE. I've been told complex analysis has all these applications in z and laplace transforms, but it seems like you only ever really need the basics like Euler's formula and algebraic manipulation of complex numbers. Contour integrals appeared in the inverse laplace and z transforms when I first learned about them, but they were brushed away as impractical when compared to using partial fractions and transform tables. Are there any cases where you would actually need some of the slightly more advanced techniques of complex analysis (e.g. residue theory), or where those techniques would provide a more practical way of doing things? I guess I'm really wondering, when do you actually use stuff like residue theory in electrical engineering?