[snogglethorpe]

Is this just the contents of the video in text form?

In any case, thanks! I don't need to watch the video now, as you've very clearly explained it in only four lines of text!

[gizmo686]

I can't tell if you are being sarcastic, but no, parent's comment is not the contents of the video. The video provides a geometric construction, and makes no use of calculus.

[snogglethorpe]

Not being sarcastic, I just didn't watch the video.

I was wondering if it was basically the same thing with nice animations...

[recursive]

It's not really any clearer to me. I cannot generalize my understanding of exponents to anything that deals with imaginary numbers.

[chombier]

For me what made it clicked is realizing that complex numbers are 2D matrices: z = x + i y = [[x -y][y x]].

So really we should be writing z = x * [[1 0][0 1]] + y * [[0 -1][1 0]], but since it's tedious we just call 1 == [[1 0] [0 1]] the 2x2 identity matrix and i == [[0 -1][1 0]], and check that i^2 = -1.

Then no more magical i number, the complex product can be derived from the matrix product, the exponential becomes the 2x2 matrix exponential, and so on.

[jacobolus]

Here, http://www.shapeoperator.com/2016/12/12/sunset-geometry/

http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf

http://geocalc.clas.asu.edu/pdf/GrassmannsVision.pdf