in synchronous generators we use a DC on the rotor then rotate it but what if we use AC while rotating the rotor won't we need less mechanical power for the rotation because of the rotational Magnetic field ?

 

in synchronous generators we use a DC on the rotor then rotate it but what if we use AC while rotating the rotor won't we need less mechanical power for the rotation because of the rotational Magnetic field ?

The mechanical power a generator requires is basically equal to the output power, since large generators are near 100% efficient.
That efficiency has little to do with how the rotating field is generated (which is what converts the mechanical power to electrical).
In other words, there's no free lunch.