= Solution
The source figure has a series capacitor followed by $R$ in parallel with $L$. Its <complex impedance> is
$$
Z=-\frac{i}{\omega C}+\frac{i\omega LR}{R+i\omega L}
=\frac{R\omega^2L^2}{R^2+\omega^2L^2}+i\left[\frac{\omega LR^2}{R^2+\omega^2L^2}-\frac1{\omega C}\right].
$$
The imaginary part vanishes at a finite positive frequency only if $R^2C>L$, in which case
$$
\boxed{\omega_*^2=\frac{R^2}{L(R^2C-L)}=\frac1{LC-L^2/R^2}.}
$$
At that frequency, substituting $R^2+\omega_*^2L^2=\omega_*^2LR^2C$ into the real part gives
$$
\boxed{Z(\omega_*)=\frac{L}{RC}.}
$$
If $R^2C\le L$, no finite positive-frequency cancellation exists; the impedance merely tends toward its high-frequency limit.
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