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

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