# symmetry-complex-plane-wave-v2.mp4

Chapter section: Primer - Complex exponentials and Wave Packets

Caption (verbatim):

The complex value rotates while its length stays fixed.

Image description (verbatim):

A complex plane wave, its two components, and the rotating value at a fixed position

## Before the animation

Chapter lines 775–775:

Here $A$ is the wave's amplitude, $\lambda$ is its wavelength, $k=2\pi/\lambda$ is its **wave number**, and $\omega$ sets how quickly the phase changes with time.

Chapter lines 777–777:

In the animation, position runs along the helix. The other two directions show the real and imaginary parts of the complex value at each position. As time advances, these values rotate and the wave pattern travels along $x$.

## After the animation

Chapter lines 785–785:

The two components are $A\cos\theta$ and $A\sin\theta$. Their values oscillate, while the length of the complex value stays fixed:

Chapter lines 787–789:

```math
|z|=\sqrt{A^2\cos^2\theta+A^2\sin^2\theta}=A.
```