Finding the waveform of current in a circuit
If you actually mean the “waveform” of the current, then it will be a sinusoidal wave of the same frequency as the voltage input except scaled and shifted by some amount. 
If you look at a phasor diagram of current and voltage of any circuit, you will notice that the current always has the same waveform as the voltage.
If you’re looking for the actual value(ie amplitude and phase shift) of the current, then yes you find the reactance and solve for i1.