> I just expect "energy" to be a number. Instead, here what we're doing is averaging complex numbers so the output is a complex number. What a complex energy means is left as an exercise to the reader.

They shouldn't be using the term energy, really. That should be reserved for the magnitude of the complex number (so re(z)^2+im(z)^2). You can write a complex number either as a real and imaginary part, or as a amplitude r (the distance you're referencing) and phase (the rotation from r+0im).

> "To find the energy at a particular frequency, spin your signal around a circle at that frequency, and find the center of mass of the plot."

As someone who's spent a lot of time with the subject, I like this better than the original.