In electrodynamics, if the form of absorption is not involved, the imaginary parts of electric field and magnetic field have no practical physical significance, just to represent the phase and facilitate calculation.

Re () is a function that takes the real part, and * means * * * yoke, which means adding a negative sign in front of the imaginary part. For example, the yoke of 2+4i is 2-4 I.

If e and h are in phase in a vacuum, they should be

S (average) =Re(E×H)/2. I didn't read the derivation you said, it's not very clear, but that's what mathematical symbols mean.

You can use the real part of the electric field and the real part of the magnetic field to calculate S completely with real numbers, and then use the complex number method to calculate S, which should be understandable. These two kinds should be the same, because the imaginary part of electromagnetic field is introduced for the convenience of calculation.

If you have studied mathematical physics methods, you should know that some integrals are calculated by deliberately introducing imaginary parts and then taking real numbers. The imaginary part of the electromagnetic field also plays this role here.