Complex Notation - Electrical Circuit

1. The problem statement, all variables and given/known data

1 (a) using complex notation, find an expression for the output voltage, v0
1 (b) using complex notation, find an expression for the input current, ig, and hence determine the phase angle of ig relative to vg

2. Relevant equations

3. The attempt at a solution
See attached two attempts, in jpgs. I've gotten myself very confused!! If someone could advise that would be great.
Attached Thumbnails

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 Recognitions: Homework Help 1.2 mH is not the same as 0.001 H; you've dropped a significant figure. This in turn has significantly altered your impedance value for the inductor, with the error propagating through your further calculations. The input is specified as a voltage source, and you've treated it as a current. This is not correct. You've then assumed that both the resistor and the inductor are conducting the entire "current" of 40A. They are in parallel so this is not possible; Parallel branches have the same potential difference, but not necessarily the same current. It's series components that have the same current.
 Thank you gneill, i'll have to look at it and perhaps get a physics tutor.