 e to the ix, what is that? It's the complex exponential, used a lot in the Fourier transform. But what is the complex exponential? It's a three-dimensional spiral. Because it's three-dimensional, depending on which angle we look at it, it can be two different things. If we look at it from the real dimension, it's a cosine wave. And if we look at it from the imaginary dimension, it's a sine wave. Using the complex exponential, the Fourier transform breaks a signal apart into the cosine and sine waves making it up.