RLC Circuit using maxwells circulating current

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a. Using Maxwell's circulating current show that

(assume that no current flows to the output terminals AB).
b. Derive the transfer function when the frequency
c. Explain, with reason, whether the output signal in part b. is in phase with the input signal and what that implies about the effective impedance of the LC combination.
Solution:
a) Writing Kirchhoff's loop equation for the first loop:
Vin = RSi1 + jωL(i1 - i2)
Vin = (RS+ jωL)i1 - jωLi2 ...(1)
Writing Kirchhoff's loop equation for ...