Finding total impedance

Question

I have a circuit as shown below

^{simulate this circuit – Schematic created using CircuitLab}

Where R1, R2 are resistors. jX1 and jX3 are reactants, and jB2 is admittance. That being said, I'm not sure how to find Zin (Total input impedance). I have 2 theories:

1. Convert jB2 to impedance by taking its inverse (Z = 1/Y) and find total impedance: $$ Zin = R1 + jX1 + ((R2 + jX3)||jB2) $$
2. Just ignore the admittance in this calculation since it's not an impedance $$ Zin = R1 + jX1 + jx3 + R2 $$

I'm not sure which one is correct. Both seem to be correct to me. Any help would be appreciated!

Answer 1

I'll convert the admittance into impedance first then treat all components as resistors but always follow the correct math with the imaginary part (j). I think that's the easiest way of doing this.