In the USA NEC the convention is to always use RMS values for steady state AC current and voltage. Also, in the USA the real part of complex power is called Average power (and many times called Real power) we don't use the word active power. When given a power factor (pf) you have to know the type of reactive VARs. So for inductive pf we use the prefix lagging (current lagging voltage) and for capacitive pf we use leading (current leading voltage). So, to correct pf you often will see the addition of leading VARs (capacitors). To take the conjugate of phasor current in polar form all that is needed is to change the numeric sign of the angle. The use of RMS values will reduce the divide by two seen when using peak values which is another type of useful mathematical simplification. So, in reality we have two beneficial techniques from Mr. Steinmetz, the AC phasor transform (which is really an application of Euler's identity) and the RMS equivalence (which is described as the effective value, equivalent heating in a purely resistive load). With the understanding that the techniques are used for steady-state AC. Given this we see that instantaneous power occurs at twice the line frequency, which is how energy (power) can move in an RLC circuit between the source and the load with a pf less than one in one cycle. I should stress that the complex power strictly relies on the use of pure sine waves. If the source is not a pure sine wave (the sine wave is distorted) then we can have differences in actual losses. Also, steady-state AC is not derived from switching on an AC source. It is a mathematical concept which assumes the effects are beyond any transient (power first applied) effects. Like transformer magnetization current.
