What is the 'characteristic frequency' of a certain impedance?
The impedance of a parallel connected resistor and capacitor is 

$$Z = R\,||\frac{1}{j\omega C} = \frac{1}{\frac{1}{R}+ j\omega C} = R \,\frac{1}{1+j \omega RC} $$

This is of the form of a resistance times a dimensionless, frequency dependent quantity.

There is a particular frequency of interest,

$$\omega_0 = \frac{1}{RC}$$

which is the characteristic frequency.  At this frequency, the impedance is

$$Z_0 =  R \,\frac{1}{1+j \omega_0 RC} =  R \,\frac{1}{1+j} = \frac{R}{\sqrt{2}}e^{-j\frac{\pi}{4}}$$