[marosgrego]

You can think of `i` as a rotation by 90 degrees counterclockwise. You do it twice and the real number line gets reflected (as if multiplied by -1). It is what multiplying by i actually does to the complex plane.

[tails4e]

Yes, the name imaginary does it no favours. I was confused for so long about i, as it was never explained on classes, and it wasn't until 3blue1brown and other math youtubers showed me the light. I really like this series on it by Welch Labs - loads of easily digestible videos, and a history lesson to boot:

https://youtu.be/T647CGsuOVU

[hamilyon2]

I like how your illustration also implies that -i is also square root of -1, which is true

[est31]

Yes! In fact, you can rotate i (or 1) by any angle around the origin and obtain a so-called "root of unity". If the angle was rational, you can now apply this rotation multiple times to itself and eventually you'll obtain 1 or -1.