I have a doubt about the physical meaning of the complex representation of electric and magnetic fields.
Let's consider an electromagnetic wave, in which both electric and magnetic fields propagate in space and time with a sinusoidal waveform of radian frequency ω.
Now let's consider their phasors E and H: they are simply complex numbers which depend only on the position (since ω is fixed and the time - dependence disappears when passing to phasors). We may represent them in the complex plane, since they have in general both a real and an imaginary part. I was told that their imaginary part represents a shift but, what kind of shift? A time-shift (delay) or a spatial shift? Or a physical rotation of the field?
Moreover, if it is a time-shift, does it coincide with the time-shift we have for instance in a circuit with reactive elements, in which for instance the phase difference between two voltages indicates that one of them is delayed with respect to the other?