For a real sinusoid,
the phasor is again defined as and the carrier is . However, in this case, the real sinusoid is recovered from its complex-sinusoid counterpart by taking the real part:
The phasor magnitude is the amplitude of the sinusoid. The phasor angle is the phase of the sinusoid.
When working with complex sinusoids, as in Eq.(4.11), the phasor representation of a sinusoid can be thought of as simply the complex amplitude of the sinusoid. I.e., it is the complex constant that multiplies the carrier term .