/sci/ - Science & Math

>>11403437
You mean de Moivre's formula?
Basically, because any nonzero complex number can be given as a double of a positive real and an element of the complex circle [math]S = \{ z \in \mathbb{C} : |z|=1 \} [/math], and the only topological group structure that the circle admits is angle addition modulo 360 degrees. Shitty source for the second result here https://math.stackexchange.com/questions/2349439/topological-groups-on-the-circle-s1

Think of it like this: you have the complex circle [math]S[/math]. You know it's closed under multiplication, and that [math]1[/math] is the multiplicative identity. Try to come up with another continuous multiplication, and notice how it "kind of preserves order", so you can "torsion it back into angle sum".
>can't you give an explanation that doesn't assume basic calc and group theory
No.
>>11403471
>assumes the reader understands why multiplication rotates by 90 degrees
Very nice, tho.