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.