802
you are viewing a single comment's thread
view the rest of the comments
[-] baggins@lemmy.ca 12 points 5 months ago

Imaginary numbers are math cope for when you're too cool to just use two numbers.

[-] SubArcticTundra@lemmy.ml 2 points 5 months ago

I never got why they didn't just introduce tuples in maths

[-] MacNCheezus@lemmy.today 11 points 5 months ago

They did, linear algebra and vector calculus are a thing, but complex numbers have certain properties that you don’t get with vectors and that are quite useful and worth studying.

[-] kogasa@programming.dev 4 points 5 months ago

One definition of the complex numbers is the set of tuples (x, y) in R^(2) with the operations of addition: (a,b) + (c,d) = (a+c, b+d) and multiplication: (a,b) * (c,d) = (ac - bd, ad + bc). Then defining i := (0,1) and identifying (x, 0) with the real number x, we can write (a,b) = a + bi.

[-] SubArcticTundra@lemmy.ml 1 points 5 months ago

Ok, that's actually quite interesting

[-] kogasa@programming.dev 2 points 5 months ago* (last edited 5 months ago)

Yup, you'll notice the only thing distinguishing C from R^(2) is that multiplication. That one definition has extremely broad implications.

For fun, another definition is in terms of 2x2 matrices with real entries. The identity matrix

1 0
0 1

is identified with the real number 1, and the matrix

0 1
-1 0

is identified with i. Given this setup, the normal definitions of matrix addition and multiplication define the complex numbers.

[-] Arrkk@lemmy.world 2 points 5 months ago

For various math reasons you only get consistent systems with 2^n dimensions, so after complex you get quaternions with 4, then the next one that works is 8, then 16, etc. They become less useful because you lose various useful features, like you lose commutabiliy with quaternions (eg ab != ba), and every time you double you lose more things.

this post was submitted on 07 Jun 2024
802 points (95.9% liked)

memes

10224 readers
891 users here now

Community rules

1. Be civilNo trolling, bigotry or other insulting / annoying behaviour

2. No politicsThis is non-politics community. For political memes please go to !politicalmemes@lemmy.world

3. No recent repostsCheck for reposts when posting a meme, you can only repost after 1 month

4. No botsNo bots without the express approval of the mods or the admins

5. No Spam/AdsNo advertisements or spam. This is an instance rule and the only way to live.

Sister communities

founded 1 year ago
MODERATORS