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 .