How can I find il in this circuit using phasor concept (Frequency Domain)?
The problem for me is with the dependent source.

Thanks

 

Is it a dpendent current source or a dependent voltage source. The symbol implies it is a voltage source but the controlling equation indicates it is a current source.

What is the controlling current. The controlling equation says "il" (or possibly "i1"), but I don't see it indicated anywhere on the diagram.

If this were a DC circuit with just a battery and two resistors, could you solve it?

 

Yes I can.
il = current of the inductor.
the dependent source is a current source.
sorry for that.

 

Then replace the voltage source with a source called Vs and the inductor with an impedance called Z_L and solve for the the inductor current I_L just as you would a DC circuit. Don't use numerical values for anything, solve it symbolically. Do that and we will take it from there.