The main insight of complex numbers is the fact that it relates exponentiation (partial multiplication) to rotation. Take that away then you might as well just

The main insight of complex numbers is the fact that it relates exponentiation (partial multiplication) to rotation. Take that away then you might as well just use matrix algebra instead. The idea is that you can “multiply by -1” not just odd or even times, but that you can do so fractionally. You can “flip the direction” partially which corresponds to shortening the original size and adding an “impetus” attribute based on the amount you shortened it by. The raisin d’être of complex numbers is the derivative theorem of Fourier transforms. In fact, perhaps imaginary numbers should really be renamed “impetus numbers”