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:
$$ \begin{align} Z_{series} &amp;= Z_1 + Z_2 + ... + Z_n\\
               Z_{parallel} &amp;= \biggl(Z_1^{-1} + Z_2^{-1} + ... + Z_n^{-1}\biggr)^{-1} \end{align} $$
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:

$$ \begin{align} Z_{COUT} &amp;= \bigg({\frac{1}{j\omega C}}^{-1}+{Z_{LOAD}}^{-1}\bigg)^{-1} \\
         &amp;= \frac{Z_{LOAD}}{j\omega C Z_{LOAD}+1}  \\ 
Z_{input} &amp;= j\omega L + R + \frac{Z_{LOAD}}{j\omega C Z_{LOAD}+1} \end{align}$$
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:
$$ Z_{output} = \biggl((Z_{VIN} + j\omega L + R)^{-1} + {\frac{1}{j\omega C}}^{-1}\biggr)^{-1}  $$