I attempted to solve the following exercise but i'm pretty sure i messed up somewhere because my answers just don't seem to add up

Can you please check my work?

Hope the pictures are clear enough

1) Express L, using R, C, and w so that R(equivalent) of AC is a pure resistor

2) Knowing that E(0)=180V, Find the amplitude of the main current I(0)

3) Find the amplitudes of U(AB) and U(BC)

Thank you in advance for your help