e^(pi*i)+1=0 - I have no idea what it means, and I’m pretty sure that no one else does, either, but it is the most profound thing that I have ever seen in my life.

>>510964811 (OP)
naively: growth to the power of complex-inverse of pi is almost exactly zero

t. sodachi

>>510964811 (OP)
Exponentiating a complex function has the effect of rotating it around a circle in the complex plane. e^xi rotates the point (1,0) (or 1+0i) around a unit circle in the complex plane by x radians.

By definition, pi radians is half a circle, since a circle has a circumference of 2pi. Rotating halfway around a circle from (1,0) lands on the point (-1,0), or -1+0i

So e^(pi*i) is -1+0i, or -1. You can restate this as e^(pi*i)+1=0, if you want your formula to look really profound because includes all these fundamental constants. But really it’s just the fact that e^xi rotates a coordinate by x radians, stated in a voodoo way

>>510965440
No it's more profound than that. Pi is not just 180 degrees "by definition", it actually works out like that if you calculate the exponential by series expansion.
It's basically a statement of how the two transcendental numbers e and pi are inherent in our understanding of what a plane is in a stupifyingly fundamental way.
You can wave any mystery away by book knowledge but that makes you a stereotypical midwit and you are missing the point.

>>510964811 (OP)
pi^2/6
if u know u know

>>510964811 (OP)
It's Euler's formula for x=pi
e^(ix) = cos(x) +i*sin(x)

>>510964811 (OP)
this is why the birthrates are low

>>510964811 (OP)
>Tfw no blacksite torturer gf

>>510964811 (OP)
Math is silly. I'm good at logic, good at numbers, but stick the two together and I'm profoundly retarded.

>>510966332
>It's basically a statement of how the two transcendental numbers e and pi are inherent in our understanding of what a plane is
It's a statement of the fact that e^xi is a rotation in the complex plane. Any time a rotation is involved, pi is going to show up, because it's the fucking circle constant. That isn't remarkable in any way.

Because of the universality of the exponential function, you can make that statement in any number of less-impressive-looking ways, it doesn't have to use 3 as the base. And because of the nature of the complex plane (where two axes are orthogonal) means multiplying by i always has the effect of rotation of some amount between 0 and 90 degrees. Multiplying a function by
>1/sqrt(2) + i/sqrt(2)
has the effect of rotating it 45 degrees. Square root of 2 is an important irrational number too, should we restate the formula to include that? We could state that
>(1/sqrt(2) + i/sqrt(2))^(2^2) + (2/2) = 0
I bet Socrates would fucking shit

>>510967415
>3 as the base
I meant e as the base. Typo. Please feel free to make ESL remarks at me now, I deserve it

>>510964811 (OP)
This is so retardedly simple to understand. Complex plane is at 90 degrees. Forget the e, use one of Euler’s formulae to replace it with an equation describing a position on the unit circle, but on the complex plane. Pi is the length of a semicircle of radius 1 that goes into the complex plane and around, hitting -1. The cosine component is 0, the sine component is -1. Add 1 to that to make it zero. The important thing here is rotating the unit circle to the complex plane.

>>510965440
>tp
bp

>>510964811 (OP)
Put away the 1 and its just a half circle on a coordinate system. Pretty simple. But amazing for reddit midwits

>>510964811 (OP)
You keep making this thread every 2-3 months. And it baits all the midwits. Respect.

>>510965440
>since a circle has a circumference of 2pi.
Not all circles has a circumference of 6.2831853072 you nigger

>>510964811 (OP)
I like turtles.

>>510964811 (OP)
Im genx and I know what this means