##### Complex Power

V and I are the voltage and current phasors(rms values)

$$\mathrm{Dummy\; Text}$$ $$\mathrm{Dummy\; Text}$$ $$\phi =\mathrm{Dummy\; Text}\xb0$$

S is the Apparent power

$$\mathrm{Dummy\; Text}$$
S = P + Q j

Where P is the real power(or average power) and Q is the reactive power

$$\mathrm{Dummy\; Text}$$
$$\mathrm{Dummy\; Text}$$
Where P is the real power(or average power) and Q is the reactive power

If V and I are the rms or effective voltage and current phasors represented in complex form.

The complex power 'S' is defined as the product of V and conjugate of I

$$\text{S = V . I*}$$ $$\text{S = P + Qj}$$ $$\text{P = |S| Cos (\phi )}$$ $$\text{Q = |S| Sin (\phi )}$$ $${\mathrm{|S|}}^{2}={\mathrm{|P|}}^{2}+{\mathrm{|Q|}}^{2}$$

I* is the conjugate of I.

S is a complex number the real part (P) is the real or average power and the imaginary part (Q) is the reactive power.

φ is the phase angle.