Comment by itishappy

3 months ago

Easier to see without the square root:

    i^2 = -1

What action when applied twice results in a sign change?

"A 90 turn" is one answer. There are probably others.

“A -90 turn” would be another.

  • Very interesting way of thinking about it, I don’t recall it ever being presented that way before. Thanks

    • Everything makes sense when you see I for what it is -- an escape from the number line rotated by ninety degrees.

      Even the roots of a parabola that doesn't hit the z axis are actually the roots of the ninety degree rotated inverse analogue hitting the imaginary plane. Since the apex of such a parabola is always centered at 0i, the imaginary places it hits are symmetric, explaining why if a + bi is one imaginary root, then a - bi is as well.

      https://teaching-math.com/unlock-the-secrets-of-complex-root...

      Again... There is nothing weird about imaginary numbers. They actually make a lot of sense. It's actually insane to only do math in one dimension when our world has three.