A Real Sinusoid: The DNA of Signals

A complex sinusoid rotating with time in the $IQ$ plane generates two real sinusoids. The question now is to produce only one real sinusoid in the complex $IQ$ plane. We start with the math and then code the expressions for visualization.

A cosine wave

A complex sinusoid with a positive frequency $\omega$ is:

$$e^{j\omega t} = \cos \omega t +j\sin \omega t$$

Similarly, a complex sinusoid with a negative frequency $-\omega$ ...