Phasor - Definition

Definition

Euler's formula indicates that sinusoids can be represented mathematically as the sum of two complex-valued functions:

or as the real part of one of the functions:

$\begin{align} A\cdot \cos(\omega t + \theta) &= \operatorname{Re} \left\{ A\cdot e^{i(\omega t + \theta)}\right\} \\ &= \operatorname{Re} \left\{ A e^{i\theta} \cdot e^{i\omega t}\right\}. \end{align}$

As indicated above, phasor can refer to either or just the complex constant, . In the latter case, it is understood to be a shorthand notation, encoding the amplitude and phase of an underlying sinusoid.

An even more compact shorthand is angle notation:

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