I have no idea what it means. I’m pretty sure nobody has any idea what it means. And it’s the most profound thing that I have ever seen in my life.
 UFOs Are A Psyop Shirt $21.68 |
 |
UFOs Are A Psyop Shirt $21.68 |
I have no idea what it means. Im pretty sure nobody has any idea what it means.
>I have no idea what it means.
>And it’s the most profound thing that I have ever seen in my life.
How do you know if you don't understand it?
It's literally just junk rotating. Honestly I find the phase explanation most intuitive, but there's a bunch of ways to think about it.
it's just a shorthand notation for
That is not how you calculate the modulus, you moron.
Rotation of unit vector by 180° (π rad.) is -1. What's hard to understand? Not really "profound" or some shit
No, it is the most profound thing we have ever seen in our lives
Rotation with respect to what dimension?
It's rotation in the xy plane about an axis in the z dimension often representing time.
Then why don't x, y, z, or t appear in the equation like they do in normal rotation formulas that involve x,y, z, or t rotations such as x = x cos θ + y sinθ and how does the imaginary dimension come into play since that is the only dimension explicitly in the formula?
>Then why don't x, y, z, or t appear in the equation
Because it's representing a relationship between the values at a fixed point. Specifically (-1, 0, π).
I think we can agree that another way the formula is written, e^(iπ)=-1 contains all three of those values, can't we? You could further rewrite it as e^(iπ)=-1+0i if you still need help.
How is a rotation a fixed point?
> e^(iπ)=-1 contains all three of those values
It doesn't contain any of the dimensions or planes you mentioned being involved in the rotation, but if you are just talking about for (-1, 0, π) e^(iz) = x + y, I still don't see how it is a rotation when rotations are more like x = x cos θ + y sinθ.
https://en.wikipedia.org/wiki/Euler%27s_formula
The word rotation does not appear anywhere in the body of that link, there is just a reference to another theorem related to Euler at the bottom.
complex numbers definitionally involve rotation. i is literally 1 rotated 90 degrees.
Anything outside of x is literally 90 degrees from x, mathematically, but in reality, spatially, rather than just theoretically, what dimension does it rotate about?
oh, you are that moron that believes that complex numbers can't be because we would then need 6 dimension(x, y, z, xi, yi, zi), god you are metaphysically moronic and detrimental for daring to waste the time of anons that attempt to comprehend what the frick is wrong with you, keep at it, you genuinely do not deserve to shake of your moronation, you, how you are right now, in terms of intelligence, is how i desire you to die in the very far future, you do not deserve to evolve mentally in any way, shape or form
shake off* your
That is how orthogonality works, dimensions are all 90 degrees from each other, which you would already know if you had spent time studying instead of seething at boogeymen since you probably realized long ago that your rotation analogy is kind of moronic when you actually try to apply it to reality, but since you have no logical way to express your claims and are too proud to admit your moronic meme is moronic, all you can do is fixate on some past argument you clearly lost and still seethe about to this day which will probably also fester until you finally stroke out over it instead of admitting that your little 3d big bang model doesn't actually explain or allow you to understand everything.
>That is how orthogonality works, dimensions are all 90 degrees from each other
thank god you are stupid, to ayone else, enjoy
So you think those axis are something other than 90 degrees from each other and you are calling other people stupid?
So you are too moronic to actually read, and instead just use the CTRL-F strategy? I don't think you're ever going to get it.
Why should I bother to read something that is unrelated to the question I asked that you only posted to appeal to authority because you know you are giving bad answers yourself and want to find an out instead of admitting you were wrong or don't actually know how to explain yourself?
>cos(x)+sin(x)
>how is it rotating???
see
x+y is specifically in the formula you gave, not sin or cos, and the rotation comes from the angle of rotation θ, not from adding the sin and cos of x.
Why can't you just explain how it is a rotation without memeing?
It's not a useful equation. It's just a natural consequence of complex numbers and polar coordinates. Nobody will ever invoke this equation to solve some other problem.
The equation is useful for trigonometry, sinusoids, and converting between coordinate systems.
Polar representation is highly useful, whenever you're dealing with multiplicative problems in C.
I find it easier to explain by putting a 1 in front of the e to show its magnitude.
Here: https://youtu.be/v0YEaeIClKY
If you have any interest at all in math, you should watch this entire channel. Grant is a genius communicator.
>this is your brain on youtube math
alternatively this is a low tier bait thread
>I have no idea what it means.
>filtered by high school geometry
>I’m pretty sure nobody has any idea what it means.
Because you are a complete idiot.
>use series representation of exp to show: e^(ix) = cos(x) + isin(x)
>recognize that r(x) = cos(x) + isin(x) parameterizes the unit circle in C
>then calculate r(pi) = cos(pi) + isin(pi) = -1 + 0 = -1
>conclude e^(ipi) = -1
There you go. Once you have the series representation, it's a straightforward thing.