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As a math person, I think this attitude is why I hated (and still do) calculus. Calculus is not a language of science, it is a branch of mathematics that is useful for science. It's description is just as static as algebra (not the least because it is algebra, just with two new functions).

Regarding the Gaussian (imaginary) numbers, they have uses which have nothing to do with rotations. My intuition for them is that they are a way of factoring expressions such as A^2 + B^2 as the difference of two squares.

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