How Does Non-Uniform Circular Motion Align with Complex Plane Calculations?

[olivermsun]

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.

 

[sophiecentaur]

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.

 

[sophiecentaur]

Vector maths works in many dimensions and in many contexts. The Complex plane is just one example of where it works, I think. You seem to be drawing the conclusion that, because the same Maths applies to your two examples then they are somehow tied together in some significant way. I don't see any necessary connection.
To return to my beans, if you follow your approach, you could say that, because two apples plus two apples gives four apples, there is some inherent connection between beans and apples.