5 ms·
> Complex numbers are about rotation. Why? (I'm not denying that it is, just pointing out that like the person I first replied to, you are jumping over the in
by creato 7y ago
> Complex numbers are about rotation.
Why?
(I'm not denying that it is, just pointing out that like the person I first replied to, you are jumping over the interesting part here and stating interesting conclusions like they are definitions.)
- garmaine 7y agoAs I said, "that's the only odd insight." I'm not claiming it's obvious, it's not. but once explained it makes sense and the rest falls in place. Here's a better resource than I can type up: https://betterexplained.com/articles/a-visual-intuitive-guide-to-imaginary-numbers/ https://betterexplained.com/articles/a-visual-intuitive-guid...
- jacobolus 7y agoA complex number “is”† a quotient of two Euclidean vectors in a plane. That is, Z = u\v is the object which when you multiply it by one vector u, scales and rotates that into another vector v. We can write uZ = uu⁻¹v = v. http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf https://geocalc.clas.asu.edu/pdf/GrassmannsVision.pdf https://geocalc.clas.asu.edu/pdf/GrassmannsVision.pdf † More precisely, the algebra of complex numbers is structurally the same as the algebra of quotients of planar vectors.