Circuit analysis Thevenin example in sinusoidal steady-state with dependent and independent ac sources
a) I think Ix =0 so you just need apply KVL to find Vth.
Then you turn off V_k, connect at the terminal a I_s = 1A => Zth = V_ABI_s
b)Open circuit at ZL then Apply KCL to find voltage across L and C that voltage is Vth
Then turn off I_s, open circuit at Zl => Zth= Z_L + Z_C
=> ZL = Zth
=> Pmax = (|Vth|^2)/8ZL