# Non-uniform circular motion

Sure, the real and imaginary parts add separately, like orthogonal components of vectors in R2:
Y + Z = Re(Y) + Re(Z) + i(Im(Y) + Im(Z)),
and so on, which allows you to use complex numbers interchangeably with 2-vectors for adding, rotating, etc. As you've already pointed out, however, some of the operations are not the same.

Gold Member
We soon get philosophical here. The reason the Maths, in all its forms, 'works' in our physical world is really quite hard to take in. Even just at the level of two beans plus two beans gives four beans. . . .
We look at vectors (2 and 3D) in spatial terms but, once you get more than 3D, you are back to abstractions. No 'direction' at all, even if there is a magnitude.

davidbenari
Well yeah, but my question was not philosophical. I think what I wrote on my diagram with the square shows why the complex plane analysis actually does represent the tangential and radial components. I thought (and still do) there was a more general way of proceeding than my diagram analysis.

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