Editing Phasor (section)

===Multiplication by a constant (scalar)===
Multiplication of the phasor <math>A e^{i\theta} e^{i\omega t}</math> by a complex constant, <math>B e^{i\phi}</math>, produces another phasor.  That means its only effect is to change the amplitude and phase of the underlying sinusoid:
<math display="block">\begin{align}
      &\operatorname{Re}\left( \left(A e^{i\theta} \cdot B e^{i\phi}\right) \cdot e^{i\omega t} \right) \\
  ={} &\operatorname{Re}\left( \left(AB e^{i(\theta + \phi)}\right) \cdot e^{i\omega t} \right) \\
  ={} &AB \cos(\omega t + (\theta + \phi)).
\end{align}</math>

In electronics, <math>B e^{i\phi}</math> would represent an [[electrical impedance|impedance]], which is independent of time.  In particular it is ''not'' the shorthand notation for another phasor.  Multiplying a phasor current by an impedance produces a phasor voltage.  But the product of two phasors (or squaring a phasor) would represent the product of two sinusoids, which is a non-linear operation that produces new frequency components. Phasor notation can only represent systems with one frequency, such as a linear system stimulated by a sinusoid.