The method shown in post #22 was incorrect. An updated method is shown here.

View attachment 296181
View attachment 296188
The v_1 and v_2 we measure with a DMM are the magnitudes, and the relationship between the measured voltage and impedance components is given by the last equation shown above. Since v_1 depends on 2 values, Z_a and Z_b, we need more than 1 measurements with different values of R's to determine Z_a and Z_b.

A Mathematica notebook showing the calculations is attached. This method, however, is unable to determine the sign of the reactive component (i.e. whether it leads or lags). The "simulated impedance " is a series combination of a 6 R resistor, a 0.7 mH inductor, and a 250 uF capacitor.