How do complex numbers appear in physics? What is their physical interpretation? How do they appear in equations of waves?

Answer by Tikhon Jelvis:

The best intuition I've seen is that complex numbers are about rotation. Basically, they take the 180° flipping that negation for real numbers represents and generalize it to rotation in a circle.

Perhaps a more general (but more vague) description is that complex numbers generalize 1-dimensional real numbers to 2 dimensions.

Take a look at How to Fold a Julia Fractal, a beautiful aricle that illustrates this idea and shows how it relates to fractals. [The visualizations require a browser and graphcs card with good support for WebGL.]

How do complex numbers appear in physics? What is their physical interpretation? How do they appear in equations of waves?

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