r8 my proof of the Pythagoras theorem. Yes, it is a valid proof

>>8572918
I don't see any proof here. I can see where you're going, but you need to write it more clearly.

I don't think it's a very elegant proof, since you're using advanced tools (Euler's identity) to prove something rather simple.

>>8572918

Elegantly retarded. 6/10.

>>8572921

It's clear enough.

>>8572929
Yes, but it's not written like a proof.

>>8572936

We're on an imageboard, faggot

>>8572941
A proof is a proof, it doesn't matter where we are. What you have there isn't a proof. At most it's an informal proof.

Yeah, that works. I mean I've seen this like 5 times already. This is usually packaged in an exercise showing that the properties of sin and cos defined through the exponential has the same properties as the classical functions.

Bretty good but you are missing many steps

>>8572918
But that's not Pythagoras theorem.

>>8572993
xDDDDD

>>8572993
... Is this b8?
[math] sin(\theta) = \frac{opposite}{hypotenuse} = \frac{b}{c}[/math]
[math] cos(\theta) = \frac{adjacent}{hypotenuse} = \frac{a}{c}[/math]
[math] 1 = sin^2(\theta) + cos^2(\theta) [/math]
=>
[math] 1 = \frac{opposite^2 + adjacent^2}{hypotenuse^2} [/math]
=>
[math] hypotenuse^2 = opposite^2 + adjacent^2 [/math]
[math] c^2 = a^2 + b^2 [/math]

I'll rate 1/10.

It's just lazy algebraic manipulation. Literally brainlet tier. Any non-retarded high schooler can do that. No geometric idea involved.

>>8573031
>No geomerty involved
>He doesn't know of the Imaginary unit circle
Z e z

>>8573002
Now this is a proof.

>>8573135
No, it's begging the question. If you procede like OP, you obviously defined cosine and sine via their series expansions. So you gotta prove formally that this is the same as the geometric definition in a triangle.

>>8573053
OP did not use any geometric argument. He only did symbolic computation.

>>8573135
No it's not.
>>8573148
This. I just carried through with what was written in the OP to show that it was equivalent to Pythagoras. It doesn't prove anything, and I also assumed that 1 = cos^2 theta + sin^2 theta without geometrically defining it.

>So you gotta prove formally that this is the same as the geometric definition in a triangle.

No one in this thread's gonna do that, which is why the OP is literally just
"This thing is algebraically equivalent to this other thing".

>>8572918
This is valid if you start with exp(z). Look at the first few pages of Rudin's real and complex analysis.