I believe it is a matter of representation of physical quantities, not of physical quantities themselves.

E.g. take voltage or current: they are scalar real quantities.
Then it has been found that using Steinmetz's transform to turn them into complex numbers makes calculations on steady-state sinusoidal quantities easier.
But a complex number is a mathematical abstraction, just even thinking of an imaginary voltage somewhere in a real circuit is totally nonsense.

Though at the end of complex calculation we can return back from representation domain to real physical quantities, get our scope and check them on real circuit.

So real scalar quantities, their complex representation which more generally can be just about anything as long as it is reversible not loosing any of the initial information and back to real life.
This is the round trip which is by the way quite common in engineering (e.g. Laplace, Fourier...)

The same may be applied to power:

In the real world (whatever it means) we have instantaneous power which is a real scalar.
Then using the same complex representation above it can be shown that multiplying voltage by conjugate current we get a complex representation S of power such as its real part P is mean power (real one) while Q, the imaginary one is reactive. $$ S=VI^*\quad P=\text{Re}\{S\}\quad Q=\text{Im}\{S\} $$

Again we have gone from physical quantities, complex representation and back to real.

So real power or complex power?

I believe it is a matter of representation of physical quantities, not of physical quantities themselves.

E.g. take voltage or current: they are scalar real quantities.
Then it has been found that using Steinmetz's transform to turn them into complex numbers makes calculations on steady-state sinusoidal quantities easier.
But a complex number is a mathematical abstraction, just even thinking of an imaginary voltage somewhere in a real circuit is totally nonsense.

Though at the end of complex calculation we can return back from representation domain to real physical quantities, get our scope and check them on real circuit.

So real scalar quantities, their complex representation which more generally can be just about anything as long as it is reversible not loosing any of the initial information and back to real life.
This is the round trip which is by the way quite common in engineering (e.g. Laplace, Fourier...)

The same may be applied to power:

In the real world (whatever it means) we have instantaneous power which is a real scalar.
Then using the same complex representation above it can be shown that multiplying voltage by conjugate current we get a complex representation S of power such as its real part P is mean power (real one) while Q, the imaginary one is reactive. $$ S=VI^*\quad P=\text{Re}\{S\}\quad Q=\text{Im}\{S\} $$

Again we have gone from physical quantities, complex representation and back to real.

@N.G.near
I see your point, but it is a matter of representation of physical quantities, not of physical quantities themselves.

E.g. take voltage or current: they are scalar real quantities.
Then it has been found that using Steinmetz's transform to turn them into complex numbers makes calculations on steady-state sinusoidal quantities easier.
But a complex number is a mathematical abstraction, just even thinking of an imaginary voltage somewhere in a real circuit is totally nonsense.

Though at the end of complex calculation we can return back from representation domain to real physical quantities, get our scope and check them on real circuit.

So real scalar quantities, their complex representation which more generally can be just about anything as long as it is reversible not loosing any of the initial information and back to real life.
This is the round trip which is by the way quite common in engineering (e.g. Laplace, Fourier...)

The same may be applied to power:

In the real world (whatever it means) we have instantaneous power which is a real scalar.
Then using the same complex representation above it can be shown that multiplying voltage by conjugate current we get a complex representation S of power such as its real part P is mean power (real one) while Q, the imaginary one is reactive. $$ S=VI^*\quad P=\text{Re}\{S\}\quad Q=\text{Im}\{S\} $$

Again we have gone from physical quantities, complex representation and back to real.

I believe it is a matter of representation of physical quantities, not of physical quantities themselves.

E.g. take voltage or current: they are scalar real quantities.
Then it has been found that using Steinmetz's transform to turn them into complex numbers makes calculations on steady-state sinusoidal quantities easier.
But a complex number is a mathematical abstraction, just even thinking of an imaginary voltage somewhere in a real circuit is totally nonsense.

Though at the end of complex calculation we can return back from representation domain to real physical quantities, get our scope and check them on real circuit.

So real scalar quantities, their complex representation which more generally can be just about anything as long as it is reversible not loosing any of the initial information and back to real life.
This is the round trip which is by the way quite common in engineering (e.g. Laplace, Fourier...)

The same may be applied to power:

In the real world (whatever it means) we have instantaneous power which is a real scalar.
Then using the same complex representation above it can be shown that multiplying voltage by conjugate current we get a complex representation S of power such as its real part P is mean power (real one) while Q, the imaginary one is reactive. $$ S=VI^*\quad P=\text{Re}\{S\}\quad Q=\text{Im}\{S\} $$

Again we have gone from physical quantities, complex representation and back to real.