Please help me solve this

Hi 

As a college student, I have been given the below task to solve

'A simulated 3-phase generator produces three voltages V1, V2 and V3 at angles of 0, 90 and -90 degrees respectively. For a balanced star load, determine the voltage of V1, V2, and V3 required to produce the same phase currents as conventional 3-phase voltage source.'

My assumption:

For simulated 3-phase

V1s = V|_0° 

V2s = V|_90°

V3s = V|_-90° therefore the phase currents

i1s = V1s / Zt |_0° - Ѳ and i2s = V2s / Zt |_90° - Ѳ and i3s = V3s / Zt |_-90° - Ѳ

where Zt - sum of line and load impedances

Ѳ - phase of total impedance

Than, in a conventional 3-phase voltage source

V1c = V|_0° and V2c = V |_-120° and V3c = V |_120°

therefore the phase current is equal to:

i1c = V1c / Zt |_0° - Ѳ

i2c = V2c / Zt |_-120° - Ѳ

i3c = V3c / Zt |_120° - Ѳ

assumprion

i1c = i1s and i2c = i2s and i3c = i3s

therefore

i1s = V1c / Zt |_0° - Ѳ where i1s = V1s / Zt |_0° - Ѳ 

therefore 

V1c / Zt |_0° - Ѳ = V1s / Zt |_0° - Ѳ

V2c / Zt |_-120° - Ѳ = V2s / Zt |_90° - Ѳ

V3c / Zt |_120° - Ѳ = V3s / Zt |_-90° - Ѳ

Does my logic make any sense?

Can I know exclude the Zt from both sides of the equation?