Beautiful way to put it! We aren't always explicit about the subject of the transformation. Similarly, when working with exponents, I think: e^ix is really 1

Beautiful way to put it! We aren't always explicit about the subject of the transformation. Similarly, when working with exponents, I think: e^ix is really 1 * e^ix That is, we're starting with 1.0 and doing a transformation (rotation) on it.