Well over 30 years ago one of the first things I learned in my EE degree was Steinmetz's method for calculating steady state amplitude and phase in AC networks comprising generators, resistors, capacitors and inductors. He worked out a transformation that lets you use simply solve a set of simultaneous equations, in exactly the same way as simpler DC networks with only batteries and resistors. The only extra price you pay is that the equations use complex numbers instead of real numbers. It really seemed like magic to me. Sadly a career in software has gradually worn down the motivation I once felt to revisit some of the really beautiful ideas underpinning technology, with the idea of getting a better understanding the second time through.