How does an impedance-matching circuit transform a complex impedance to a resistive impedance?
Why A complex load looks like a resistance in series (or parallel) with a reactance. A matching network uses reactive components to present an equal and opposite reactance, canceling the load's X so the net reactance is zero, and at the same time it transforms the remaining resistive part up or down to the value the source wants to see (typically 50 ohms). That is the definition of a conjugate match: if the load is R + jX, the network makes the source see R - jX plus the transformation, leaving pure resistance. Because the parts are ideally lossless inductors and capacitors, no power is burned doing this.
Watch out The idea that reactive currents are dissipated in matched resistances is wrong because a proper matching network stores and returns that energy in L and C rather than turning it into heat; dissipating it would defeat the purpose. Negative resistance and transconductance are active-device concepts and have no role in a passive L, T or pi network.
Match = cancel the X, transform the R. Two jobs, both done with lossless L and C.