Wasn't some sort of engineering-grade complex analysis part of your EE (undergraduate?) curriculum? I am sort of surprised Euler's formula would be a "secret weapon" in EE classes.
Most practically oriented engineering students bitch about the math heavy parts because they don't have any use for them. They are happy with just the formulas and arithmetic. They can calculate electronic circuits, do Laplace transforms and Fourier transforms mechanically. As long as they understand what goes in and what comes out, it works just fine.
You'd think so, but it wasn't. Closest we got was probably the linear systems course, but that wasn't super close. I did a little more math than usual in that I took real analysis as an elective, but I wasn't able to squeeze complex analysis in.