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The average power over a time‐period T in any time‐harmonic periodic signal is [J.5, B.10]

(2.1.106)

where the time‐harmonic instantaneous voltage and current waveforms are

(2.1.107)

The voltage and current in the phasor form are written as follows:

(2.1.108)

A complex number X = a + jb has its complex conjugate, X^* = a − jb. Thus, the real (Re) and imaginary (Im) parts of a complex number are written as follows:

(2.1.109)

On using the above property, the instantaneous voltage and current are written as follows:

(2.1.110)

The average power in phasor form is obtained from equations (2.1.106) and (2.1.110),

(2.1.111)

It can be expressed in the usual AC form,

(2.1.112)