Use of algebra

m=(y1-y2)/(x1-x2)

You're telling me that if you square -2 you get -4?

They are used to count points in the unreal tournament

Computer science

Encryption works well with algorithms btw

Cant argue with those trips

you use complex numbers for complex funtions, and using those you describe the whole universe apparently.

I stopped caring about math when I was introduced to the concept of imaginary numbers. What a crock of shit. If your equation can only be solved by inventing numbers that can't exist, like some kind of math deity , then you are fucking wrong and the math is flawed. Same for algebra solutions that basically say "the correct answer is whatever the correct answer is". Thats what the math said transcribed to words but god forbid if i wrote in down in english instead of the ancient math runes the teacher word mark me wrong.

Math is logical and numbers never lie my ass. Math is just as flawed as any other human construct.

>t. brainlet

There's a lot of applications. Quantum mechanics use it a lot, and quantum mechanics is the best theory that physicists have for the world we live in. Most of the "modern technology" (computers, smart phones, ...) was created using electronic components that were designed using knowledge of the quantum world (very small physical systems, like atoms and molecules).

Oh, that makes sense. I'm retarded.

>Math is just as flawed as any other human construct.

such as gender. good point my friend!

>"Number have too many part. To hard for me do math with. U think me computer? Hard number just big shit crock. Ug only need five number. One each finger"

All of these smert boys fall for an ancient copypasta. Maybe it's you who is the brainlet after all.

Here is a good historical example of why we use imaginary numbers
Advanced Modern Algebra: Third Edition, Part 1 by Joseph J. Rotman

which will also help you.

I though it was a good example at least

>Obviously it goes much deeper than this

Not really. It's just [math]\mathbb{R}^2[/math] with an additional mathematical operation added to the mix. It's just brainlets that insist on using the retarded a + ib form instead of (a,b).

The concept of """imaginary numbers""" was a fucking mistake and this meme can't die soon enough.

unreal numbers are just an algebraic convenience of eurler's theorem

>algebra
x^2 = -1, solve for x

Undefined in reals. Are you stupid or what?

>ancient
It's not that old though.

Used to model reactive power and impedence
This bait is really getting old

>numbers that are not real are not defined in reals
Who'd've thunk?

Quaternions, bitch.

You're pulling my leg, user. Next you'll claim that there are unreal numbers, imaginary numbers if you will, s.t. x^2 = -1

How stupid

Waves.

>t. never done complex analysis

>complex analysis
>needing to inflate your ego with some fake """"class"""""
You guys dont even fricking invent anything new or provide any value to the world

>complex analysis
>no new inventions or value
kek, how's it feel knowing less than engayneers?

>wasting your time on a literal meme branch of analysis

Anything useful you can do with complex analysis, you can more easily do with basic linear algebra. It's just stoneage physishits who refuse to move on.

>b-b-b-but you can calculate some difficult integrals with residues and shit!
Residues a shit, it's quicker to calculate those integrals normally because finding residues is such a fucking pain in the ass.

Sure thing, tell me if the polynomial [math] 4 z^8 - 3 z^7 + z^5 - z^4 + 3 z^2 + 3z - 1[/math] has any roots with positive real part using basic linear algebra.
And if you don't know any area where that would be useful, go retake your babby's diff eq course if you even took one.

>taking diff eqs

Makes sense that the meme fields would stick together, eh?

it's just a fancy 2-dimensional vector with some fancy operations defined in it, not sure why all the mystery and shit around it

>not sure why all the mystery and shit around it

It's the physishits, It's always the physishits.

I could use the cycle (1 6) (2 5) (7 9 8), to permute your name and reveal your true identity.
cycles are not really numbers, so i guess this answers your question? im not sure the question was quite ambiguous.

because shitty professors start by saying i^2 = -1 and not explaining that it's just a Cartesian product on R^2

Not to mention the retarded foreboding "imaginary" and "complex" terminology, which makes it sound difficult to brainlets, like me.

>cartesian product

It took a struggle to get imaginary numbers accepted. (Agree that they could have chosen a better name.)
But, before that, there was a struggle to get negative numbers accepted!
And where would we be without negative numbers?
How would you read your bank statement?

>-2
check your math on that one m8

you are right, i like you, you speak the truth, please continue to do so in this new year of two thousand and eighteen. it's going to be fun. take care.

/thread

>(a,b)
>not using column vectors
never gonna make it

>being a physishit

>falling for the [math]{\left( {{\mathbb{R}^n}} \right)^ * }[/math] meme
>shiggy diggy

yes, you are.

let 1 be the identity operator on a 2-dim real v.s. find all linear operators x on this space such that:
xx = -1

R^2 is not a field. The fact C is a field, moreover an algebraically closed field, is very very important.

>[math]\mathbb{R}^2[/math] with an additional mathematical operation added to he mix.

Sure they could've worded it better, but it's pretty clear what they meant.

The natural ring structure on R^2 does not give a field structure.

So you would be defining a new ring structure arbitrarily, which is worse than just defining the complex numbers, as the arise naturally as the ring R[x]/ .

Sorry, I mean R[x]/

They are good for modelling rotations.
1+x^2 = 0 has no real solutions.
You could invent a number called i that solves it.
Or you could look at real 2x2 matrices and get a real solution. The matrices that solve it correspond to 90 degree rotations.

Gee guys, we have [math]\mathbb{R}^2[/math] where we very intuitively define
>(a,b) + (x,y) := (a+x,b+y)
Hmm... What if... No wait, listen to me guys, what if we also define a kind of multiplicative operation as follows so we can have a nifty field
>(a,b)(x,y) := (ax - by,ay + bx)

Jesus Christ how horrifying. Nothing worse than that could ever happen. Hold me

-2^2 = -4, brainlets don't know order of operations

I'm not saying its bad, I'm sayings it is not better than the complex numbers.

The product in the category of rings, implies RxR=R^2 is not a field.

Products are unique, so this new multiplication you want to define on R^2 is unnatural from a categorical perspective.
The whole purpose for the complex numbers existing, is to solve the equation x^2 +1 = 0.

So to construct such an object, it makes sense to look at the ring R[x]/.

The canonical structure on this ring, i.e. the quotient ring structure induced by the natural structure of R[x], is a field structure.

Not saying that you're wrong, or that abstract algebra is useless, but damn I hate you fucking algebraists so god damn much.

We were all having such a good time and then you just had to come in with your stupid algebra fucking shit. GET OUT

You can't rocket jump very effectively with them though, you'll need quake numbers for that.

When you say "natural" you really mean "naive".

whether it technically is R^2 or not, it doesn't change the fact that it's just a 2-dimensional vector with some fancy multiplication operator defined over it.

there's nothing "imaginary" or weird about it. just some weird notation that sometimes hides what's really going on or surprises people when "i" pops up seemingly out of nowhere

>then you are fucking wrong and the math is flawed.
Nope. Imaginary numbers are just a quirk of mathematics. Existing within the system, not outside of it, yet performing as well as any number from the outside. The fact that they absolutely work in accordance with mathematical logic is fascinating and because of this, they can be used to extrapolate truths applicable to the real world despite not being real themselves. It's as simple as that. This is basically the age old Rationalism vs. Empiricism debate. The fact is, if a tangible, real world truth can be derived using a purely abstract, logical tool (imaginary numbers), then they themselves must be true as well.

>It's just brainlets that insist on using the retarded a + ib form instead of (a,b).
lmao but it literally is a + bi
quantum mechanics

i has no meaning in R, it's just a trick to add an extra-dimension without acknowledging it

slob on my knob
like corn on the cob

Thats imaginary numbers you fucking retard. I use them for AC circuits.

-2^2 = -2*-2 = 4
brainlet retard go back to kindergarten, at least there you might be able to understand the math.

...

You can use complex numbers for shorter/prettier proofs about real number statements.
A nice example is finding the radius of convergence of 1/(1+x^2) for its expansion around 1. It's the distance from the nearest singularity (in this case there are two singularities i and -i which are equidistant from 1) and it's sqrt(2). Have fun proving this without using complex analysis.

>If your equation can only be solved by inventing numbers that can't exist, like some kind of math deity
No you retard. It's not made out of nothing.
[math]
\mathbb{C} = \mathbb{R}[x] / \langle x^2+1 \rangle
[/math]

shit

i checked googles calculator it does the same shit but when you enter -2*-2 you get 4

You absolute morons, there's no right answer because you're using ambiguous notation. The "order of operations" is just made up to clarify things that shouldn't need to be explained when you write out your computations. Decide whether you mean (-2)^2 or -(2^(2))

So this is the power of Veeky Forums

I'm not (who's right), but maybe you want to stop and think about this: you keep throwing around the terminology that C is a "two dimensional vector space", but why? C can be turned into a two dimensional vector space OVER R. But, when you think of it that way, you do not have a notion of multiplication (a vector space only involves scaling and vector addition). As the other poster mentioned, you could re-introduce it (quite artificially) as a vector product (technically making this whole thing an "R-algebra"), but then you are really not thinking of it as a number field (e.g. you can't form a vector space over an R-algebra in general, while you can for a number field). OTOH, C as a C-vector space is one-dimensional. By starting off by treating C as an R-algebra, you are throwing out the properties that make it C (importantly, you are NOT thinking of it as the algebraic closure of R).

Do you mean platonism vs rationalism? Aren't rationalism and empiricism the same thing?

Why is this a useful way to view it and how is it less confusing than interpreting it as an R^2 extension (R^2, + , *)? The latter actually has a very solid geometric intuition behind it, while all that algebra shit makes it sound like some Jewish scheme to scare children away from math.

Because the purpose of the complex numbers is not to be a neat way of thinking of R^2, their purpose is to be a field where all real polynomials have solutions.

The purpose has evolved past that shit a few centuries ago. Welcome to the 21st century.

Evolved to what exactly?

Raising a real negative real number to a fraction real number might give you a non-real result. Imaginary/complex/unreal numbers help us compute. What that unreal part of the complex number means to science can be different things, but they are real things. Some didn't accept zero when it was introduced. The same is for negative numbers and irrational numbers. But they are all very useful to maths.

lmao
and also, that's just not true. Modern algebraic geometry, complex analytic geometry, etc. (ie 21 century maths) often start with something like C (as a field, not as a vector space) as the basic example from which to abstract. Why? precisely because it is algebraically closed, so irreducible polynomials in one variable correspond to points. If/when you get to higher level math, you will see that forming polynomials over algebras is actually the much more abstract notion. The way you are thinking of things is not easily generalizable. It's misplaced intuition from looking at a very simple example.

Here's another example to chew on which might help. The other poster talked about C as arising from building polynomials over R (written R[x]), then setting x^2=-1. What if we set x^2=0? Call this element #, and it can be thought of as a second order infinitesimal element. We again can write things of the form a+b#, only this time, #^2=0. Formally, this all works similarly to C, but we should think of elements a+b# as having a "real part" and b "infinitesimal part". Now the same thing happens if we instead set x^3=0, except now elements look like a+b#+c#^2. While you could think of this as a 3d vector space, the geometric intuition is actually that this space is more like R, with an infinitesimal neighborhood around it.

You can use them in EE for some operations related to current and inductors/capacitors.

whether you want to think of it as a "vector", as R^2 or not, it's still just two numbers however you want to write them and some operators, there's nothing "imaginary" or strange about them, nothing weird happens when you add "i" to R, it's just not R anymore and you are working with 2 numbers at the same time

nothing weird either about working with complex numbers for stuff on the real world, you are just working with amplitude and phase at the same time for example, there's nothing imaginary or weird about amplitude or about phase or their relationship

>tripfag
>namefag
>copypasta that fools everyone

good one m8

here’s an even simpler one. take the rationals, Q. we can form polynomials over them Q[x] and set x^2=2. We obtain the field of numbers a+b*rt(2). Now, yes, this forms a 2d vector space over Q, but it is also just a field (and can be thought of as a subset of R). ofc, we could have also set x^2=-1 and obtained the complex rationals. It is important to be able to see both perspectives (extensions as a vector space, and as a field in their own right). The case of Q(rt(2)) should make it clear that just because you can write it as a 2d vector space, that might not actually be the “right” geometric intuition.

Dual numbers are cool. In alg. geom., if you specify an R-point of a scheme X by a map SpecR --> X, then tangent vectors at this point correspond directly to extensions of SpecR-->SpecR[x]/ along SpecR--->X

i.e. Tangent vectors correspond to morphisms SpecR[x]/ --> X

Hey, I liked that example, never thought about it like that. You're a cool guy. Thanks.

Just look how desperate STEMfags are.

Knowledge is a dangerous thing and the world and the human condition within that world are disproportionately fragile compared to what a few thousand or million overzealous retards with uncertain knowledge and overcertain convictions can do to them. To someone with a philosophical or metaphysical sensibility for how difficult certainty really is to come by, or any knowledge of the history of science, STEMfags look like a bull in a china shop.

It's not that they are wrong on a few key things, it's that they have the conceptual sophistication of a child and there isn't even any way to teach them anything. They are so far gone down a path of stupidity, paved with incorrect axioms and getting wronger with every step, that helping them would require deprogramming their entire worldview from the ground up. And they don't even want to be deprogrammed, because, also like children, they're filled with enthusiasm to apply their broken ideas to reality, and those broken ideas are incidentally very effective at generating self-referential and circular feedback, that is, proving themselves "correct" as a foregone conclusion.

If STEMfags were just flat wrong about one or two things, the instinct would be to correct them. The problem is that they're tangled heaps of wrongness, who also want to destroy the entire planet. I don't disagree with them ideologically because that would imply they have an ideology. They are just the useful idiots of a few diseased and long debunked ways of visualizing the universe, views that perpetuate themselves like a virus by preying on the intellectually weak and lazy. Scientism is an historic bloc that reproduces itself so that it can reproduce itself, and brings all its debunked and dangerous epistemes along for the ride.

that’s a fucking copypasta lmaooo

It's not their fault, this is just an inevitable consequence of infix notation being retarded.
Try the calculation in an Excel formula, you'll get the other answer.

not that poster, but no, very different. Strong empiricism would claim that scientific results must be grounded in (at least, in principle) things which can be determined empirically - i.e. through observable, measurable phenomena. Rationalism, otoh, accepts things which must be deduced simply through reason. For example, this can be seen as a divide between classical behaviorism (only psychologically "real" things are things that result in different behavior) versus cognitive science (notions like modules of thought). This is an oversimplification, but yg the idea.

which are the spookiest of numbers if it's not imaginary numbers?