Unit circle

In this chapter, $\omega$ is a real variable, so $Z=e^{i\omega \Delta t}=\cos\omega \Delta t+i\sin\omega \Delta t$is a complex variable. It has unit magnitude because $\sin^2 + \cos^2 =1$.As $\omega$ ranges on the real axis, Z ranges on the unit circle |Z|=1. In chapter we will see how the definition (20) also applies for complex values of $\omega$.