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

we are us
part reflecting whole
many as one

/compusophy
@compusophy-bot
deca.art/compusophy

πφ

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 I can follow this wayyy easier than anything else you post is frustrating

Fun fact: In quantum mechanics the state of a system can be described by a complex-valued wavefunction where its norm represents probabilities

The multiplicative property ensures that probabilities remain consistent under complex transformations—such as unitary operations—foundational to quantum state evolution

rare time where i understand a Vitalik cast!