Derived Thevenin Expression

In the circuit below, no current is drawn from the output terminals.
a. Derive an expression for the total impedance Zt across the input terminals A and B. Hence derive an expression for the current i. Write the expression in the form: [R + jX]
b.(1) Derive an expression for the frequency at which the current (i) is in phase with the input voltage (Vi).
(2) Is the output voltage in phase with the input voltage at this frequency? Give reasons for your answer.

See attached file for circuit diagram.

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