What is the physical meaning of it [the imaginary part of an impedance] ?

The physical meaning is the phase shift between voltage and current. When the voltage and current through a load are perfectly in phase (phase shift zero), there is no imaginary part. Or else said, that is a resistive behavior.

Image source:

https://en.wikipedia.org/wiki/Electrical_impedanceIf you think about impedance as in the above plot, Z is the impedance, R is the resistive (real) part, X is the reactance, and Theta angle \$\Theta\$ is the phase shift between U and I.

XL and XC (for ideal L or C) are always at 90 degree, so they point either up or down. An ideal resistor R can not introduce phase shifts, it's angle is always zero (horisontal). When different resistive values R (resistors) and reactance values X (capacitors or coils) are combined together, the result is a complex impedance Z as in the picture (those are all vectors, so X and R add up as the Z seen in the picture), and the resulting Theta angle will be different from just -90, 0 or +90, as if it were for a single ideal component. Which one is up and which one is down (XL or XC) might depend by convention (which is taken as reference, voltage or current), but usually we measure voltages, so XL is pointing up in that complex impedances plane (XL has positive sign), and XC is pointing down (negative sign) in the complex plane from the above picture.

When we match impedances, we want something (either an L or a C) such that it compensates for the already existing X (being it up or down), such that the resulting Z is pure resistive (Theta zero). In other words, we want the

*complex conjugate*, or much clear in physical meaning words, we want the opposite component:

- If the behavior is capacitive, so an XC vector pointing down, we identify the XC vector lenght, and use an equal size vector pointing up, so we need a coil with an XL of the same length. The result is that they cancel each other, and there will be no phase shift between I and U. Already existing R vector will remain there, horizontally. The resulting circuit will behave as a pure resistor (the usual 50 ohms, but can be other values too).

- there is another aspect, in case of 2 ideal resistive circuits, for maximum power transfer (or else said for zero energy reflected back), the two of source and load must have the same value. So the complete rule (in AC) for matching is to have complex conjugate impedances. If one is A+jB ohm, the other must be A-jB ohm, so according to that complex impedance plane posted above, when putting them together, +jB with -jB (the reactances) will cancel each other, and only the pure resistive part (A = A = 50) will remain.