Kinda funny, I was thinking about the idea of explaining imaginary numbers to high school students by saying "actually, there's no magic.

Reply to Kinda funny, I was thinking about the idea of explaining imaginary numbers to high school students by saying "actually, there's no magic. on Sat, 11 Apr 2026 13:53:59 GMT

boydstephensmithjr@hachyderm.io — Sat, 11 Apr 2026 13:53:59 GMT

@stefanie @gregeganSF @ZachWeinersmith I got lucky in HS I did have one maths teacher that looked up a "long-hand square root" and taught it to me, tho I never got good at it.

But, I think a lot of the generation that would be teaching me maths hadn't learned square-root long-hand, and the students that were interested in such stuff where taught roots on the slide rule.

Reply to Kinda funny, I was thinking about the idea of explaining imaginary numbers to high school students by saying "actually, there's no magic. on Sat, 11 Apr 2026 13:45:41 GMT

merovius@chaos.social — Sat, 11 Apr 2026 13:45:41 GMT

@ZachWeinersmith The thing that irks me about the "i is the solution to X²+1=0" explanation is, that it is unclear *which* of the two it is (and whether it matters).

Reply to Kinda funny, I was thinking about the idea of explaining imaginary numbers to high school students by saying "actually, there's no magic. on Sat, 11 Apr 2026 13:44:18 GMT

merovius@chaos.social — Sat, 11 Apr 2026 13:44:18 GMT

@ZachWeinersmith Explain ideals and construct ℂ as ℝ[X]/(X²+1).

I actually do think this is (appropriately simplified) a far better explanation than the "add an imaginary i". Especially if you go all the way ℕ→ℤ→ℚ→ℝ→ℂ. because once you get to ℂ, the quotient construction is already familiar.

Really, the actually weirdest and hard to understand step is ℚ→ℝ, which is also the most badly explained in school.

Reply to Kinda funny, I was thinking about the idea of explaining imaginary numbers to high school students by saying "actually, there's no magic. on Sat, 11 Apr 2026 13:37:34 GMT

mausmalone@mastodon.social — Sat, 11 Apr 2026 13:37:34 GMT

@ZachWeinersmith Also, for the love of god, explain to them that they're called "imaginary" because they're NOT REAL NUMBERS.

It's a pun. It doesn't actually mean anything.

Reply to Kinda funny, I was thinking about the idea of explaining imaginary numbers to high school students by saying "actually, there's no magic. on Sat, 11 Apr 2026 13:36:47 GMT

mausmalone@mastodon.social — Sat, 11 Apr 2026 13:36:47 GMT

@ZachWeinersmith If you're introducing it, I would start with a number line. Explain that all real numbers are there. Now show them that sqrt(-1) is not there.

Now, assuming that's a number at all, you can multiply that number by any real number and you get a second number line. 1i, 2i, 3i, etc ...

EXCEPT 0 times anything is 0. So those two points have to be the same. That's when you erase the second number line and make it vertical. THAT'S where your complex plane comes from.

Reply to Kinda funny, I was thinking about the idea of explaining imaginary numbers to high school students by saying "actually, there's no magic. on Sat, 11 Apr 2026 13:36:30 GMT

wlm@mastodon.gamedev.place — Sat, 11 Apr 2026 13:36:30 GMT

@oblomov @ZachWeinersmith Yeah it’s important to realize that they aren’t matrices per se, but matrices are one way to represent them (same with tensors). But maybe not yet in high school.
(NB not a mathematician, so apologies for any sloppy terminology.)

Reply to Kinda funny, I was thinking about the idea of explaining imaginary numbers to high school students by saying "actually, there's no magic. on Sat, 11 Apr 2026 13:28:32 GMT

stefanie@social.anoxinon.de — Sat, 11 Apr 2026 13:28:32 GMT

@gregeganSF @ZachWeinersmith I remember the maths teacher in school telling us that square roots can not be calculated, but you can only guess, then square, guess again, and get closer.
I always thought that to be BS, but never dug deeper because I already had a calculator back then.

Sometimes I wonder where I would have gotten in life if I had real teachers, instead of these bottom of the barrel failures.

Reply to Kinda funny, I was thinking about the idea of explaining imaginary numbers to high school students by saying "actually, there's no magic. on Sat, 11 Apr 2026 13:26:44 GMT

wlm@mastodon.gamedev.place — Sat, 11 Apr 2026 13:26:44 GMT

@ZachWeinersmith I always liked the escalating order of discovery*:
1 + x = 1? Zero
1 + x = 0? Negative numbers
3 * x = 1? Rational numbers
x * x = 2? Irrational numbers
x * x = -1? Imaginary numbers
x * y - y * x = 1? Quaternions
(xy)z - x(yz) = 1? Octonions
where every step is a 🤯.

(*or invention if you will)

Reply to Kinda funny, I was thinking about the idea of explaining imaginary numbers to high school students by saying "actually, there's no magic. on Sat, 11 Apr 2026 13:25:51 GMT

gregegansf@mathstodon.xyz — Sat, 11 Apr 2026 13:25:51 GMT

@stefanie @ZachWeinersmith

There are many different ways you can do all of these things!

Reply to Kinda funny, I was thinking about the idea of explaining imaginary numbers to high school students by saying "actually, there's no magic. on Sat, 11 Apr 2026 13:20:23 GMT

stefanie@social.anoxinon.de — Sat, 11 Apr 2026 13:20:23 GMT

@gregeganSF @ZachWeinersmith Wait. That's what sqrt(2) is? Literally?

Reply to Kinda funny, I was thinking about the idea of explaining imaginary numbers to high school students by saying "actually, there's no magic. on Sat, 11 Apr 2026 13:15:59 GMT

oblomov@sociale.network — Sat, 11 Apr 2026 13:15:59 GMT

@Wlm @ZachWeinersmith you can do it without matrices by going with rotations. And by going the Geometric Algebra route, one can even develop frameworks where everything (complex numbers, split-complex numbers, quaternions etc) can be derived the same way.

Reply to Kinda funny, I was thinking about the idea of explaining imaginary numbers to high school students by saying "actually, there's no magic. on Sat, 11 Apr 2026 13:10:07 GMT

wlm@mastodon.gamedev.place — Sat, 11 Apr 2026 13:10:07 GMT

@ZachWeinersmith I’d say matrices are more confusing, and you’re gonna need the i notation later anyway.
You can’t write reals either in a conventional way, so technically they’re weird too! (I realized later.) The whole “real” and “imaginary” names are a little misleading, but that’s a discussion that’ll quickly derail into philosophy.
[edit: it helps to realize that a significant part of the reals are literally called “irrational” ]

Reply to Kinda funny, I was thinking about the idea of explaining imaginary numbers to high school students by saying "actually, there's no magic. on Sat, 11 Apr 2026 12:54:30 GMT

gregegansf@mathstodon.xyz — Sat, 11 Apr 2026 12:54:30 GMT

@ZachWeinersmith

Some people will find the algebraic idea simpler, some people the geometric.

Some people will like the argument “You know how there is no rational number you can square to get 2, but we can introduce a number with that property and see where it takes us? Let’s do the same thing with a number you can square to get minus one, as well!”

And some people will like the argument “You know how multiplying by minus one takes you 180 degrees around zero on the number line? Let’s introduce the idea of multiplying by something that takes you 90 degrees around zero, which sort of makes us have to have a number plane, and see where *that* takes us!”

Reply to Kinda funny, I was thinking about the idea of explaining imaginary numbers to high school students by saying "actually, there's no magic. on Sat, 11 Apr 2026 12:40:57 GMT

dryak@mstdn.science — Sat, 11 Apr 2026 12:40:57 GMT

@ZachWeinersmith (I am sure you'll manage before recess)

Reply to Kinda funny, I was thinking about the idea of explaining imaginary numbers to high school students by saying "actually, there's no magic. on Sat, 11 Apr 2026 12:40:08 GMT

dryak@mstdn.science — Sat, 11 Apr 2026 12:40:08 GMT

@ZachWeinersmith > "POOF, a rotation matrix appears"

Next step: quaternions.

Reply to Kinda funny, I was thinking about the idea of explaining imaginary numbers to high school students by saying "actually, there's no magic. on Sat, 11 Apr 2026 12:39:54 GMT

oggie@woof.group — Sat, 11 Apr 2026 12:39:54 GMT

@ZachWeinersmith
Yeah we think of imaginary as something that can't exist, doesn't exist, etc, but that's not what they are.

Getting past the name was the tricky part, I think

Reply to Kinda funny, I was thinking about the idea of explaining imaginary numbers to high school students by saying "actually, there's no magic. on Sat, 11 Apr 2026 12:39:40 GMT

gbargoud@masto.nyc — Sat, 11 Apr 2026 12:39:40 GMT

@jernej__s @ZachWeinersmith

I could easily be remembering wrong, it was over 20 years ago

Reply to Kinda funny, I was thinking about the idea of explaining imaginary numbers to high school students by saying "actually, there's no magic. on Sat, 11 Apr 2026 12:37:45 GMT

jernej__s@infosec.exchange — Sat, 11 Apr 2026 12:37:45 GMT

@gbargoud @ZachWeinersmith Was pretty similar for me, though IIRC it was all over a single lesson.

Reply to Kinda funny, I was thinking about the idea of explaining imaginary numbers to high school students by saying "actually, there's no magic. on Sat, 11 Apr 2026 12:37:07 GMT

paradox@raru.re — Sat, 11 Apr 2026 12:37:07 GMT

@ZachWeinersmith
I think about imaginary numbers as combining with real numbers to make 2D numbers.
They're not imaginary, the name just stuck cuz somebody was weirded out by them.

Might be a bit off.

Reply to Kinda funny, I was thinking about the idea of explaining imaginary numbers to high school students by saying "actually, there's no magic. on Sat, 11 Apr 2026 12:35:57 GMT

gbargoud@masto.nyc — Sat, 11 Apr 2026 12:35:57 GMT

@ZachWeinersmith

The way I learned it in school, we kept i as sqrt(-1) (dropping the +/- for simplicity) for a few lessons before the teacher introduced i as a convenient notation for it and eventually called it imaginary

Reply to Kinda funny, I was thinking about the idea of explaining imaginary numbers to high school students by saying "actually, there's no magic. on Sat, 11 Apr 2026 12:34:24 GMT

justinh@twit.social — Sat, 11 Apr 2026 12:34:24 GMT

@ZachWeinersmith

Reply to Kinda funny, I was thinking about the idea of explaining imaginary numbers to high school students by saying "actually, there's no magic. on Sat, 11 Apr 2026 12:32:41 GMT

zachweinersmith@mastodon.social — Sat, 11 Apr 2026 12:32:41 GMT

Like is "there's this thing called i and it's 'imaginary' but we can use it like any other number" more or less intuitive than "you're sitting here doing algebra and suddenly a number explodes into 4 numbers"