I said that any calculation in electrodynamics CAN be done without imaginary numbers, I never said that it would be the most common or convenient way of doing things.

If you use a different form of solution to maxwells equations, electrical impedance can totally be expressed as just another real property. Fourier transform also is not necessary to solve maxwells equations or any other physical systems. It just might make it significantly easier and more convenient.

Obviously imaginary numbers existed and where used way before quantum mechanics was a thing but they werent technically necessary in physics because they never appeared in the equations of fundamental theories (Maxwells equations, general relativity, newtonian mechanics)