It doesn't help that i is given names like "imaginary" and "complex". We may as well call them "too-hard-for-you" numbers, and laugh condescendingly when students ask about them.

Same with quaternions and dual quaternions. They perform rotation and scaling in 3D space. Calling them "hypercomplex numbers" makes it sound like an advanced concept only to be understood after years of dedicated study.

I get that naming things is hard, but they could have gone with something that didn't sound like it was intended to stroke the egos of the learned few who understand.

I prefer the term rotor, because they perform rotation. The actual math involved isn't that difficult if you've learned the basics of geometric/Clifford algebra.

Someone on HN proposed "Lateral Number" which I thought was a good one. It's a number, just to the side of the numbers you know.

"If we call +1, -1, and √-1 had been called direct, inverse and lateral units, instead of positive, negative, and imaginary (or impossible) units, such an obscurity would have been out of the question."

--Gauss

One of the most helpful things for me when handling imaginary and complex numbers came not from a math class, but a physics class. My HS physics instructor said rather than "imaginary" we could think of -1 as a "hidden" number, because after you do the math fairly often you see where the number would be, but you just can't see it among the "real" numbers. This was literally an aside to something else he was talking about at the time.

Calling the imaginary numbers "lateral" and saying they were "to the side of" other numbers would've been helpful, too. I'm not sure it would have been quite as helpful to me, personally, but either is better than "imaginary" just to juxtapose with the "real" numbers.

> My HS physics instructor said rather than "imaginary" we could think of -1 as a "hidden" number, because after you do the math fairly often you see where the number would be, but you just can't see it among the "real" numbers.

IIRC you often encounter a system where the energy is constant, but only if you consider the imaginary part of some equation holding the potential energy, which then exchanges with "actual" kinetic energy.

Somehow I missed the √ symbol in √-1 there but I think it was understood I meant i, not -1.

To add to this, a website I've found useful is betterexplained.com. Specifically for complex numbers, take a look at [1] and [2]. But they also have good articles with visualizations to help you understand the Fourier transform, the number e, integrals and derivatives, linear algebra, etc. A starting point is [3]. One useful idea is that they color the different parts of math equations to explain each part separately, see [4].

Another great source of math visualizations is the YouTube channel 3Blue1Brown, in particular the series on linear algebra [5]. (I didn't intuitively understand what a determinant represented or what the determinant of a transformation being zero really meant, until watching [6].)

[1] https://betterexplained.com/articles/a-visual-intuitive-guid... [2] https://betterexplained.com/articles/intuitive-arithmetic-wi... [3] https://betterexplained.com/articles/developing-your-intuiti... [4] https://betterexplained.com/articles/colorized-math-equation... [5] https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2x... [6] https://www.youtube.com/watch?v=Ip3X9LOh2dk&list=PLZHQObOWTQ...

While it has been multiple decades now since I've been in school, this by far, was the best explanation I've read on how/when/where/why of imaginary numbers. I don't recall ever hearing polar anything related to discussions of "i". Thanks. You've now filled my "learn something new every day" quota.