A $4-$pole, $3-$phase permanent magnet AC machine is fed from an inverter that can provide up to $380$Vll$.$ The motor has IF $=30$A and LM $=45$mH$.$ Its stator current cannot exceed $40$A$.$ If the motor operates in the field weakening region with the field weakening component of stator current equal to $25\%$ of the value of IF $,$

a$.$ What is the maximum value of the torque producing stator current component?

Iq $=39\mathrm{.}29$ A

b$.$ What is the DC input voltage, assuming six$-$step operation of the inverter?

Vdc $=487\mathrm{.}18$ V

c$.$ What is the angle $?$

$=100\mathrm{.}81$

d$.$ What is the magnetizing current?

Im $=45\mathrm{.}2860\mathrm{.}2$ A

e$.$ Draw the phasor diagram, including labels and values.

Please show all work, answers are provided.