How to find the impedance of this RLC circuit?

Complex impedances that are purely series or parallel can be lumped similar to groups of resistors: $$ begin{align} Z_{series} &= Z_1 + Z_2 + ... + Z_n\ Z_{parallel} &= biggl(Z_1^{-1} + Z_2^{-1} + ... + Z_n^{-1}biggr)^{-1} end{align} $$

The problem is that your circuit has 3 nets defining input and output, so it cannot be lumped as a single impedance; we can solve this by modeling a source across the input nets and/or a load across the output.

Borrowing my diagram from a similar question:

$$ begin{align} Z_{COUT} &= bigg({frac{1}{jomega C}}^{-1}+{Z_{LOAD}}^{-1}bigg)^{-1} \ &= frac{Z_{LOAD}}{jomega C Z_{LOAD}+1} \ Z_{input} &= jomega L + R + frac{Z_{LOAD}}{jomega C Z_{LOAD}+1} end{align}$$

This gives the impedance seen by $V_{IN}$. To determine the impedance from the load's perspective, you have to account for the impedance of the source:

$$ Z_{output} = biggl((Z_{VIN} + jomega L + R)^{-1} + {frac{1}{jomega C}}^{-1}biggr)^{-1} $$

^{simulate this circuit – Schematic created using CircuitLab}

Redrawn circuit with the specified condition applied. The impedance looking in is $frac{Delta P_0}{Delta Q_0} = R + j omega L$. The capacitor has no effect since the voltage at the top right node is now fixed by the constant voltage source $P_l$.

If the assumption of constant $P_l$ is wrong, then the impedance calculation shown above is invalid. It is better to add a general impedance $Z_{nxt}$ in parallel with the capacitance to represent the input impedance of whatever comes next in this circuit. And re-calculate the impedance (you wont need $P_l$ or $Q_l$ for that calculation since they have been modelled by $Z_{nxt}$).