math

https://x.com/AlgebraFact/status/1802110136472817917

This identity simple, but shows important fact: the norm for complex numbers is multiplicative

(a+ci)*(b+di) = (ab-cd)+(ad+bc)i

norm(x+yi) = sqrt(x^2+y^2)

So

(ab-cd)^2+(ad+bc)^2 = norm((a+ci)*(b+di))

(a^2+c^2)(b^2+d^2) = norm(a+ci)*norm(b+di)

The two are equal

If we're keeping things real, positivity and negativity are the two roots of unity. Negativity is the more primitive one.

But if things get more complex, then you can identify an even more primitive root of unity - but it requires using your imagination.

The fact that the imaginary number 'i' is actually useful in some real world electro magnetic equations suggests that current mathematics is not yet an accurate description of the universe and its workings. 

But how do we evolve the math required to improve our understanding of the workings of the universe? There are extreme edge cases, like the centres of black holes, that may require extending math quite a bit...