Recall Euler's Identity,

Multiplying this equation by and setting , where is time in seconds, is radian frequency, and is a phase offset, we obtain what we call the

Thus, a complex sinusoid consists of an ``in-phase'' component for its real part, and a ``phase-quadrature'' component for its imaginary part. Since , we have

That is, the complex sinusoid has a

The derivative of the instantaneous phase of the complex sinusoid gives its instantaneous frequency

- Circular Motion
- Projection of Circular Motion
- Positive and Negative Frequencies
- Plotting Complex Sinusoids versus Frequency
- Sinusoidal Amplitude Modulation (AM)

- Sinusoidal Frequency Modulation (FM)

- Analytic Signals and Hilbert Transform Filters
- Generalized Complex Sinusoids
- Sampled Sinusoids
- Powers of
*z* - Phasors and Carriers

- Importance of Generalized Complex Sinusoids
- Comparing Analog and Digital Complex Planes

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