A $3-$phase, $8-$pol, $50$ Hz$,6600$ V$,$ star$-$connected synchronous motor has a synchronous impedance of $0\mathrm{.}66+$j $6\mathrm{.}6$ Ohms per phase. When excited to give a generated emf of $4500$ V per phase, it takes an input of $2500$ kW$.$ Calculate:

i$.$The electromagnetic torque$$

ii$.$The input current and power factor$$

iii.$$ The load angle$$

iv$.$ If the motor were to operate at an input current of $180$ A at unity power factor, what would then be the value of the internal generated voltage under these calculations$$