The goal is to calculate i3.

I know that e3(t)=200sqrt2cos(wt)

C=1mF w=1000rad/s

P=10kW Q=10kVAr

P*=10kW Q*=-5KVAr

What I'm doing:

e1(t)=200sqrt2cos(wt-120)

e2(t)=200sqrt2cos(wt-240)

i3+i3'(capacitor)=i3''(load)+i3'''(load*)

i3'=V2(phase)/Zc

i3''=S/(sqrt(3)*VL)

i3'''=S*/(sqrt(3)*VL)

My doubt is in i3'' and i3'''

i3'=200sqrt2e^j(-240º)/j=283e^j(30)

i3''=10000sqrt(2)e^j(45)/sqrt(3)sqrt(3)200sqrt(2)e^j(30)=1,6e^j(15)

i3'''=11180e^j(27)/sqrt(3)200sqrt(2)e^j(30)=22,8e^j(-3)

Is this procedure correct? Thanks