Think of what school does to pupils. Most of them got scared away from mathematics by their teachers. So am I. After school everyone find his way to avoid mathematics in his regular live. Due to this nearly noone is watching these fabulous videos. But it' s like in the Navy. You have to challenge your fear.

and then you upload a 2 second clip of google translator failing at pronouncing "kurzgesagt" and get a million views.😐

@@VitaMoonshadowOLD 💔

crazy edo mathematical videos are some of the most consistently well performing videos on this platform. Seeing as the quality of his videos are genuinely amazing it’ll only be a matter of time before he snowballs into the same popularity as say 3b1b

He has 18k now

we here bhaiya😬😂

Nice name

They are identical operations.

Blender

Just forgot ¯\_(ツ)_/¯

It was probably manim

I think that the numbers were rounded when they were displayed on the screen.

I think you're assuming that the phi symbol is representing the golden ratio, which, in the case of this video, it isn't. It's just representing a real number for the phase of the complex number.

I actually used Blender, I wouldn't be able to make the fuzzy number things in Manim.

@@JoshsHandle Ah fair enough. So even the equations are Blender-made?

@@4sety I use a plugin that lets me type LaTeX in Blender's text editor and then click a button to convert it into a mesh.

I call them "spherical numbers" because i is the fundamental constant of spherical geometry. It also has a few cousins like j from the split-complex numbers, which are also often called "hyperbolic numbers," since j has exactly the same connection to hyperbolic geometry that i does to spherical geometry. (See if you can find what an equivalent would be for flat Euclidean geometry. Hint: it's not the ℝeal numbers.)

Neither. The imaginary component is really just a part of the single value. The better way to think of complex numbers in reference to quantum computing is not as a real and imaginary component but as an amplitude and a phase (rotation). The amplitude in quantum mechanics is what's actually relevant and is what determines the probability of something being true while the phase is the property that fundamentaly makes these computers quantum because it is what determines how two numbers interfere with each other (add). So two amplitude 1 numbers added together could be anywhere between 0 and 2 in amplitude depending on their relative phase.

There is nothing wrong with "complex." A complex is anything composed of more than one part. Complex numbers have two parts compared to the simple pure-real or pure-imaginary numbers, which only have one part.

Easiest would be to treat them like vectors: real numbers are one-dimensional (have one component). Complex numbers are two-dimensional (have two components). Purely imaginary numbers are also one-dimensional, but on an orthogonal axis, so I've heard them called "lateral numbers."

Because quantum mechanics likes to go spinny, and complex numbers are _the_ way to represent spinny.

Court-gas-sight maybe???

curts-geh-saght

If there was such a function f:C~{0}-->R (a function from the non zero complex numbers to the real numbers, as we don't care about magnitude and just the phase or argument (however you want to call it) then we can argue this about the complex numbers of the unit circle. Having that said if there was a continuous function "f" from the unit circle to the real numbers such that for every z in the unit circle, f(z) is an argument of z, by the formula this video is about we will have that z = e^(i*f(z)) = cos(f(z)) + i*sin(f(z)) (the last equality is euler's formula) then we will have that this function is injective, and also surjective over its image, therefore bijective over its image. There are some basic results in a branch of math called topology that say that if have some type of space and a continuous function from this type of space to another different, then its image will have the same "type". For those interested the properties or types of spaces that are preserved by continuous functions are topological properties. Well there are two topological properties that are really important, one is connectedness and the other is compactness. It can be proved that the unit circle is connected and compact (in the usual topology) we have that its image has the same properties, but there are some results in topology that say that the subspaces of the real numbers that are connected are those that don't miss any point in between those numbers that are in the subspace (this means [a,c[ U ]c,b], i.e. the interval [a,c] but missing a point b in between, is not connected) otherwise the subspace is connected. For the compact subspaces of the real numbers we have that those are precisely the ones are bounded and closed ( this means that the extremes of the interval have to be finite and the points in the extremes have to be in the subspace). So a connected and compact subspace of the reals has to be an interval [a,b] where a and b are finite. The thing is that by reasoning above, we have that the image of that function f has to be interval [a,b] as we said before, but if we take out a point of the unit circle and take the image of that resulting set (something like cutting band or a ring), this set is still connected, but its image that is something like [a,c[ U ]c,b] (because f is injective) with c being the image of the missing point in the unit circle, but this set is not connected, so we have a contradiction, therefore the function that we started with cannot exist. Ps: I am sorry if something is not well written or I have missed something, but I had to omit some details, english is my third language, its almost 4am in my country and I am a bit drunk. I don't really why I am writing this. I hope it makes someone get some interest in this kind of things.

Antimatter: 💀

You can, you can think of equally big forces against each other, where one points in the positive direction and the other one in the negative direction. If you add these forces, you get x-x=0.

They are just a relation between 2 dimensions. If you have 3 dimensions, then there are 3 different relations between them. Both also need an extra component to describe how much to do nothing for a total of 2 and 4 components respectively. ... wait. That's just the quaternions!

You are mixing up different uses of the word "dimension."

​@@trappedcosmos No.