Why are E and B field in phase in far-field electromagnetic wave propagation?
The impedance of free space is not a complex impedance quantity; it is resistive with a value of \$120\pi\$ or about 377 ohms. This means that the magnitude ratio of E to B is 377:1 and, each are linked in phase to one another due to that non-complex resistance. If you expect a full derivation of Maxwell's equations on this site, you are expecting too much - try stack exchange physics.