Prove to me that complex numbers aren't arbitrary circlejerking bullshit

Is this a bait thread? A simple google search will find enough applications for complex numbers to shut you up.

Can your real numbers do this?

most brain dead faggots live on credit. balancing a check book becomes taking your $500 paycheck and decided who to pay (whos interest charges to pay) with the money.

people are retarded, do you honestly think "rent to own furniture" stores and Paydays stores make a profit based on the small amount of people who need new furniture because of a flood? go look at /g/, most are burger flippers yet have a $3000 battlestation

>buy $1500 couch with $50 down
>no payments for 1 year
>1 year later they cant pay it off
>35% interest rate and principle payment with back interest
>"oh hai repo men!"

Can real numbers derive solutions to 2nd order differentials?

Ah, k, well I live in a social democratic country (Germany) people don't do loans unless they buy a house

provide roots to all integer polynomials

also try looking at differential equations, you know those things that are everywhere.

The complex numbers are the smallest algebraic closure of the reals. Also, complex cobordisms are intimately tied to chromatic homotopy theory and algebraic K-theory. Plus, the complex numbers are an algebraic artifact from the "complex" Hopf fibration, so they are very natural and show up a ton when reasoning about why certain patterns arise in the homotopy theory of the spheres.

This. Underdamped responses would be a hassle without Euler's formula.

Even with people pushing for a sort of unification of homotopy theory and logic itself, I have a hard time putting it of strange topologies over field theory.

Prove to me that numbers aren't arbitrary circlejerking bullshit

>protip, you can't

>the matrix ([1,1],[-1,1]) doesn't exist
ok

>HUR HUR REAL NUMBERS ARE REAL
>IMAGINARY NUMBERS ARE FAKE

All numbers are equally unreal you retard.

What the fuck did you just fucking say about complex numbers, you little bitch? I’ll have you know I stopped caring about math when I was introduced to the concept of imaginary numbers, and I’ve been involved in numerous secret raids on Al-Gebra, and I have over 300 crocks of shit. I am trained in equations that can only be solved by inventing numbers that can't exist and I’m the top math deity in the entire US academic forces. You are nothing to me but fucking wrong. I will wipe you the fuck out with math the flaws of which have never been seen before on this Earth, mark my fucking words. You think you can get away with saying that shit to me over the Internet? Think again, fucker. As we speak I am contacting my secret network of algebra solutions across the USA and your IP is being traced right now so you better say "the correct answer is whatever the correct answer is", maggot. The math that says the pathetic little thing transcribed to words. You’re fucking dead, kid. I can be anywhere, anytime, and I can mark you wrong in over seven hundred ways, and that’s just if you write it down in english instead of ancient math runes. Not only am I extensively trained in unarmed combat, but I have access to the entire arsenal of the United States Logical Math Corps and I will use numbers that never lie to their full extent to wipe your miserable ass off the face of the continent, you little shit. If only you could have known what unholy flaws your little “clever” human construct was about to bring down upon you, maybe you would have held your fucking tongue. But you couldn’t, you didn’t, and now you’re paying the price, you goddamn idiot. I will shit complex numbers all over you and you will drown in it. You’re fucking dead, kiddo.

because thanks to "invention" of complex numbers you can shitpost on your phone

This picture is a great representation of intuitionist logic. Saved.

they sure help with the description of underdamped circuits but you're probably too much of a fag to know about that

Why aren't there any responses to this? I'm an EE, and complex numbers literally take up most of our calculations which have physically verifiable effects in the real world...

You're exactly right. Complex numbers can be realized as pairs of real numbers (a,b) with certain properties like
(a,b)=(c,d) iff a=c and b=d
(a,b)+(c,d)=(a+c,b+d)
(a,b)*(c*d)=(ac-bd,ad+bc)
from the last property:(0,1)*(0,1)=(-1,0)
if we choose to define (0,1)=i for notational convenience then i*i=-1 and (a,b) is equivalent to a+bi.

they can also be realized by matrices ([a, b],[-b, a]) a+bi

which is a specific instance of the more general form [eqn]a+b\sqrt{N}[/eqn] being ([a,b],[bN,a]) where N=-1

>I have a hard time putting it of strange topologies over field theory.

literally what

/////////////thread

The original historic reason for the complex numbers was not to solve the equation [math] X^2+1=0 [/math] despite what you hear in classes. The reason for them was to solve degree three polinomials, look here
>en.wikipedia.org/wiki/Cubic_function#General_formula

Even if you have real solutions, the intermediate steps involve manipulation the "fake" numbers, and yet you end up with the correct solution. That is exactly what you're asking for.

>link goes to calculating square roots
>literally the necessary step in solving general quadratics
>somehow this is magically different

The solutions for the quadratic were understood since antiquity, you don't have to invent the complex numbers when you can just say when they have no solutions.
And the necessary step involving quadratics is exactly what I said, the point is that the imaginary part coming from two different square roots can cancel out, and you get a legitimate real solution.

you can't be posting without complex numbers. checkm8 faggot.

>can't solve x + 2 = 0
>make up "negative numbers" like -2
>pulling numbers out of your ass to be able to solve equations
>someone actually defends this
I knew math was a joke once some autists decided there must be more than the natural numbers

if complex numbers aren't real then explain this
[math]\frac{\sqrt{2}+\sqrt{2}*i}{2}[/math]

Some people say "imaginary numbers" is unfortunate naming. I insist it's a good thing since it keeps the plebs out.

define:
[math]\mathbf{1} = \begin{bmatrix}
1 & 0 \\
0 & 1

\end{bmatrix}[/math]

also define:
[math]\mathbf{i} = \begin{bmatrix}
0 & 1 \\
-1 & 0

\end{bmatrix}[/math]
you will find that these two definitions will satisfy the identity:
[math]\mathbf{i}^2 = -\mathbf{1}
[/math]
Consider complex numbers as a linear combination of these two matrices:
[math]z = a\mathbf{1} + b\mathbf{i} [/math]
We have now defined complex numbers solely in terms of real numbers. These can be used to solve many problems in engineering and physics. A popular shorthand is to drop the boldface:
[math]z = a + bi[/math]

what now OP?

This

they are found in nature

for example impedance calculations

>he thinks 'are found in nature' is the same as 'are used by humans to model nature'

w e w

e

w

l a d

a

d

>balancing a checkbook
>useful

automatized already

>he thinks there's a difference
w e w

e

w

l a d

a

d

prove to me that "real" numbers aren't arbitrary circlejerking bullshit

fucking this
everyone who doesn't understand that all mathematics is a set of rules which can be used to model reality needs to pull their no math head out of their asshole

no

you're late

Prove to me that negative numbers exist.

Give me one real, physical example of a negative number.

And don't give me some shit like "Oh I have -$2000 in my bank account". No, you have $0 in your bank account and you owe $2000 (a positive value).

Negative numbers do not exist in reality. Mathematicians just made them up.

No numbers "exist". Complex numbers are imaginary in the same way that negative numbers are imaginary.

It was probably a bad idea to call i the "imaginary number".

God i love this thread!

Most people will live rich full lives and never have a need to apply imaginary numbers. That is also true for irrational and basically negative numbers. But the need for all of these types of numbers is real. In the case of imaginary numbers the need is very subtle and complex. Which makes their need, and therfore existence, very hard to explain to non-math folk

This video series explains why we use them very well.

m.youtube.com/watch?v=T647CGsuOVU

>responses
>to real sci/math
you seemed to have mistaken this board for a non-shitposting one

If we just taught students that [math]\mathbb{C}^n \cong \mathbb{R}^{2n}[/math] from the get-go I bet we wouldn't have threads like these.

Not a "math person" but know a fair bit, tell me if this is flawed thinking in some way:

While I can't think of any non-mathematical or computational use for numbers like i, it seems to me that there doesn't need to be a "why" as in a purpose for them to exist, their existence is self evident in the logic of numbers. Square roots and negative numbers both exist insofar as any mathematical concept exists, it stands to reason a negative number has a square root and we should be able to mathematically express it. I was never really confused by them conceptually for this reason, it seemed very natural that -1 should have an expressible square root.

And maybe this is only because I'm a little younger than most here (19), but no one in school ever had a problem with negatives. I think it was explained to us that it could represent debt, which I guess was concrete enough that no one complained that "lol never gon use this something something balance checkbook :DD" and zone out.

the problem is introducing square roots, square roots are generally as unbelievable as complex numbers and should be introduced at the same time in the same way

The common that square root of 2 is not rational still assumes it exists, which in my opinion remains to be proven. Square root of 2 is taken on faith for many years, perhaps forever, before any kind of retarded construction of reals is ever taught. But finite field extensions of rationals can be introduced basically at the exact same time as matrices, and in fact are probably a really good motivation for introducing them in the first place.

>people are still answering my thread almost 6 hours later
didn't expect this

this is the only correct answer
Am mathematician

This is why I have no furniture except for a mattress on the floor at my 1br apartment.

>can't solve equations like x-1=1
>invent "natural" numbers like 2 to have vacuous answers to problems with no solutions
>math autists literally have no clue what they are talking about

Look mom, I'm shitposting with the cool kids!

The exact reason, the kernel of it
youtu.be/gCAxGTt7nLg?t=11m25s

Baisically yes.

Math people say pretty much what you said but like this:

It doesn't "make sense" that you can take the square root of a negative.

it does have meaning.
for example, imaginary power is power that was transmitted but never used (reactive power).
so it has a real world application and a real world meaning, meaning it's not worthless.

You can't. Square root is a simple redneck function that doesn't even claim to be able to do that.

[math] \displaystyle
\sqrt {x^2} \ne \pm x, \quad \sqrt {x^2} = \left | x \right |
\\
\left | x \right | =
\left \{
\begin{align}
x, & \hspace{1em} x \geq 0 \\
-x, & \hspace{1em} x < 0
\end{align}
\right .
[/math]

Only if you get lucky.

I gotta be real, I'm 23 and I have no idea what "balancing a checkbook" means. Is this an American thing?

>paying taxes?
shit comes out of my income automatically.
>paying off credit cards
a matter of transferring enough money from one account to another

what is it?

All numbers are imaginary and intangible.
Do any of you guys think they are real?

wow realy maeks u think

Here's my two (2) apples.
Now show me your i (i) apples.

I means putting math involving strange topologies conceptually and logically before something "pure" as fields.
To say complex numbers are natural because they arise in some relatively complicated settings is not a convincing point

But that's wrong unless you set up a quite strange structure on R^2n (the one isomosphic to C^n as a vector space) where pairs of numbers from different rows get involved with each other upon scalar multiplication.
Uf you don't mean isomorphism by that sign but just bijection as sets, then
C^n = R
is true just as much.

strawman

If complex numbers were bullshit then most of our models of electronic circuitry, signal processing and so on would be totally incorrect which does not seem to be the case. They are one of the more heavily used things at least in electrical engineering and without them the work they do would be extremely difficult

you're a complex guy

for you

All math is arbitrary circlejerking bullshit made up by humans to represent relations found in nature and elsewhere. However, as it is consitent in a good description of nature and is usefull to us, we do not render it arbitrary circlejerking bullshit.

>EE
>doesn't understand that your complex number calculations are just glorified trigonometry
Leave the conversations about complex numbers to the people that actually understand them :^)

show me your -2 apples.

show me the logic behind i^2 = -1

You would first have to identify what an apple is.
By following logic, you will find there is no apple.
There is no boundary as such. It is only your imagination creates that. Thus, your "2" apples are imaginary.

I define i to be the number which when squared = -1

how unfortunate that some guys thought it clever to call the numbers "complex", "real", "imaginary", "rational", "irrtational", "natural", etc.

...

As another mathamatican
All of math is circle jerking. You make up sets, usually of numbers, and decide on the rules that apply to operations within that set. Bla bla

Some times the problem requires only gives meaning to natural numbers like savages trading beads.

Sometimes you need to divide land and you use the the real numbers. Allowing you to figuring the area of a circle.

And sometimes you need to work with the complex numbers.

There is no logic behind why i^2=-1. There is no logic to why in calculus we get to pretend infinity is a thing. Whenever mathmagians are presented with a problem you get to decide what set of numbers you want to work with and what properties you want them to have. It just so happens that when you are working on some problems using complex numbers just works.

so yall nailed it. we mathmagicians circle jerked them int exsitance. just like we did with other insane shit that everyone swallows. My favorites are -1x-1=1 the existance of 0 and the irrational numbers.

So when a problem arises that we know has a solution, and no tools work. We sit around circle jerking and and reading math papers until we abitraraly will numbers to behave a certain way. then if our new load of the good stuff magically solved the problem; we unload it all over the world like the intilectual bukkake the plebs deserve!

Describe the relationship between current and voltage in an oscillating circuit without using imaginary numbers.

>Everyone swallowing the reals
lurk more

Oh yeah swallow more!
those irrational numbers. They totally make sense.
*glug*
I bet you like 1+2+3+4+...=-1/12 too.
*Glug*
Oh god quit talking and swallow more of my circle jerked math.
Ooo
Hyoerbolic geometry!!!!
Oooh god
1 isnt prime!!
Oooo Swallow swallow.

....
....
Ahh that was medium good.

idiot

Well, it literally does make sense to me. But thanks for letting me know that intuitively understanding a relatively simple math concept is wrong somehow.

i = -1^1/2
literally highschool level math, not sure why you're on this board if you don't even understand that

>nihilism
;^)

Stupid negger

Is that nihilism?
I don't know. I havn't read much into it. maybe I should.
Im danish, so I could easily read Soeren Kierkegaard.

I just know that what I say is true in the sense that it is coherent. At least according to how I percieve it.

at least im right

It's often called Nihilism. Basically it's the thought that nothing is truly distinct from anything else, at it's most extreme everything is just a system of energy and particle reactions and any further definition is imposed by humans. Basically anti-platonism.

It's different than Nietzsche's nihilism, which is his description for the anti-value system between when the "old order" collapsed and when a new order would rise up, almost totally unrelated.

yes, there are two apples in the picture, but how that that prove the existance of a number two? there being TWO apples is a property (a quantitative property, in this case). in a similar manner, complex numbers are used to represent a property of something, be it a physical or an abstract object

You can use them to prove shit like trig identities desu.

>It's often called Nihilism. Basically it's the thought that nothing is truly distinct from anything else, at it's most extreme everything is just a system of energy and particle reactions and any further definition is imposed by humans.

I'm uncertain that particles can exist. Wouldn't that be impossible to determine?
I mean, they would have no real boundary. They would just consist of smaller particles, that themselves would consist of ever smaller particles into infinity.
Following logic, it would mean that everything amounts to nothing, and nothing amounts to everything.
That is what the unified field is all about, and why they can't come up with a theory.
They are quantifying that which is unquantifiable.

>there is no logic to why in calculus we get to pretend infinity is a thing
>mathamatician [sic]

What the fuck is an apple? They're just concepts made up by humans. The only things that actually "exist" are quantum fields. All else is abstraction done by humans to make our models simpler.

>balancing a checkbook
"Balancing a checkbook means you've recorded all additions (deposits) made to your account and subtractions (withdrawals). Each deposit and withdrawal is called a transaction. The purpose for balancing a checkbook is to know how much actual money you have in your checking account at any given time."

Seems worthless with the advent of online banking.