Good old Gauss said that if you could understand this identity with just a quick look at it you were "et le caput dolent friggin pinata fribee", wich roughly translates to "certainly a witty man ".
What do I need to know to test my might?
Don't get me wrong, I'm FULL ON about this numbers thing but the letters really mess the whole deal.
What does that "e" even mean?
"i" as an exponent? Hold it right there chieff, too much numbers for today
>>8108682
It's pretty straightforward. It's just the polar expression of z=-1. https://en.m.wikipedia.org/wiki/Complex_number
You can prove that you can express numbers like this with the Taylor series of sine and cosine.
>>8108682
All you need to understand this is the modulus-argument form and/or the cos+isin form. Usually these are learnt with De Moivre's formula.
It's pretty early on in any material regarding complex numbers.
Euler's identity is the Beatles of equations
Overrated as hell (not bad, just overrated) and hyped up by plebs that only know mathematics up to calculus
>>8108682
Well shit, man. If you don't know what [math]e[/math] means, then you're in for a real shock about what [math]i[/math] means..
>>8108752
what does 0 mean?
>>8108762
It means [math]e^{\pi i} + 1 [/math] cancel out.
>>8108682
i have a question senpai, was oiler gaub really smart?
>>8108750
Edgy
The definition of e^x for a complex number x is by a power series, so an infinite sum of complex numbers. If you do it right, is fairly easy to see that the formula is true, bc things cancel out. Apparently he had an intuition for it based on multiplication in the complex plane being just rotation by an angle and scaling, and thought that if you don't have that intuition you're not for to be a mathematician.
>I'm FULL ON about this numbers thing but the letters really mess the whole deal.
irony is making /sci/ an ugly place
I've seen way too many irony threads these days and sadly most of them have been of very low quality
>>8108800
nope that's a meme, he stole the patent for the laser from maxwell and sold it to the russians, he's only praised because that helped them defeat the nazis
>>8108682
you must feel good about all those people not realising you're a troll OP :^)
This Real nigga is not dumb
>>8110060
>if poteyto
>then pomtahtoe
yo watch doin meyn dis no injective map, bro, YO, y u invertin thang that no change by puttin 2pi on it, YO, SUP, MANG? y u sayin men brunch aff logamorithm is only brunch, brah??
>>8110069
I'm sorry, I don't speak swah-nigger. Can you please speak English?
>>8110075
and yet this nigger is less retarded than you when it comes to basic calculus.
>hurr lets invert a periodic function
>DURRR
>>8110121
Lieb
>>8108750
This. The Stone-Weierstrass is honestly more beautiful and useful than Euler's Identity Not to say it's shit, but it's overrated.
