AC analysis: finding L and R
You are basically treating all components as resistors, just that their impedances are expressed as complex values.  That works.  Keep at it.

Banging around complex values can be a pain, but it should get you there in the end.

In some cases, you can get away with simpler formulas for the equivalent resistance to get the same magnitude current.  Keep in mind there will be a phase shift between voltage and current, but if you only care about magnitudes then the "resistance" of a capacitor is 1/&omega;C, and for a inductor &omega;L.