>yfw there is an entire branch of mathematics dedicated to "analysing" completely made-up numbers that have literally no physical representation in the real world Friendly reminder that if you still take imaginary numbers seriously in 2018 you are a hopeless brainlet.
And before retards start coming in to debate this, please tell me how to get this this mythical realm of yours where one can possess 7 + 9i apples.
Friendly reminder that mathematics isn't even slightly concerned with what things do and do not have a physical representation in the real world. If that causes you to not take it seriously, then perhaps you should try to actually understand some math before criticizing it.
Gavin Smith
>EE >fuckloads of imaginary shit that is real >Matsc >lots of imaginary shit that is real >anything dealing with oscillatory systems and ODEs has fuckloads of complex analysis Congrats on completing algebra 2 brainlet
Leo Sanchez
>what is reactance legit u work with imaginary numbers semester 1 electronic engineering
damn op is dumb
Benjamin Powell
>no physical representation >trigonometric functions not showing up all the time when describe oscillations >euler not giving us connections between complex numbers and trigonometric functions >no physical applications It's like you've never taken diff EQ before.
James Howard
Can't you imagine apples? Just grab 7 real apples and then imagine 9 apples next to them and you're done.
Oliver James
hahaha complex no. are useless lel *gimbal locks*
Ryder Ortiz
Quantum states are complex, so its literally physics
The observables in a quantum system are the eigenvalues of the Hermitian operators acting on the quantum state. And those are always real numbers.
Ayden Torres
Just because it's not observable doesn't mean it's not useful; I'm sure you like computers and transistors working
Angel Walker
I agree, but op asked for an actual physical representation (which exist anyway as just points in a plane).
Kayden Cox
>no physical representation in the real world The amount of ontological assumptions here is off the wall. What exactly does it mean for an abstract entity to have a "physical representation in the real world" if I may ask? Let's take some arbitrary abstract object and call it OogaBooga. What would it mean for OogaBooga to be a "representation" of, say, a particular tree?
Lucas Allen
Physics use it anything involving: rotation, waves, vibrations
>because rotation are related to waves by the formula: [eqn]r \ e^{i\theta}=r \ (\cos{\theta}+i\sin{\theta})[/eqn]
>Since Electricity behave as waves: EE uses complex numbers ALL THE TIME
In Circuits, Electromagnetic Waves, Electronic Signals >with lots of applications in real world, since without such math no one would figure out how to make modern electronic devices as computers or smartphones
Joseph Robinson
Well "real" numbers aren't anymore physical than "imaginary" numbers.
Numbers dont exist at all. So why take issue with just one group?
Ryder Miller
>Physics use it anything involving: rotation, waves, vibrations *Physics use it in anything involving: rotation, waves, vibrations
Noah Gray
>Numbers dont exist at all.
Eli Martinez
Euler rotation in matrix form is still limited by rotation order
Levi Cooper
t. literal brainlet
Luis Moore
they're literally just pairs of real numbers with multiplication defined so that (0,1)*(0,1)=(-1,0) stop being retarded
Nicholas Ramirez
>faggot Why the homophobia?
Chase Ramirez
You can't have -7 apples retard. Or even 2/3 apples. >but you can have a apple debt or a fraction of an apple Then you're talking about debts and fractions of apples, not apples. They're meant to "count" or rather represent different things.
Grayson Martinez
Holy fuck. What is even the point of this argument? There is no reason to try to redefine such a concept so narrowly when its inherent meaning is already obvious. Do you think you are realistically going to convince anyone to come around to this backwards-ass manner of thinking?
Adrian Morales
>What is even the point of this argument? The point of this argument is that everything you said after those words applies in EXACTLY the same way to OP's argument about complex numbers. It's a reductio ad absurdum.
Nathaniel Williams
Complex numbers are just vectors in in R^2. You can have an apple lying in the position 7+9i relative to you.
Andrew Jones
Oh, whoops. I thought you were being serious.
God, I swear someone here unironically claimed that same thing in a different thread. This place is so confusing.
Henry Williams
they're useful for rotations, op
say [math]1 + 1i[/math] represents the point (1, 1)
all you have to do to rotate it [math]n[/math] degrees is multiply it by [math]cos(n) + sin(n)i[/math]
so, for example, to rotate it 45 degrees, all you do is
so you new point would be [math]0 + i\sqrt{2}[/math], i.e (0, [math]\sqrt{2}[/math])
don't you think that's comfy? in the real world you might want to rotate some apples from something, complex numbers are a tool you can use.
Noah Lee
implying real numbers exist also theyre useful for like cubic roots etc
Jace Morris
>retards ITT failing to grasp the point Obviously you can use fake math to do shit with oscillations, rotations, electrical currents, vectors, waves, etc. That's not the point. The point is that, when I rotate my phone 90°, I'm not multiplying it by i. What you're doing is making an abstraction that happens to use imaginary numbers. You are taking my phone's coordinates, using fake math to convert it into complex numbers, multiplying that by i, then turning that back into actual real physically-representable coordinates. What I want to know is where I can actually physically find i in the universe. Are there two shoes a distance of i meters apart somewhere? An apple with mass i kg? A rocket that fell to the ground after i seconds? No? Then it's fake.
Numbers absolutely exist. I have 9 apples. I have 6 + 3 apples. I have 12 - 3 apples. I have 3 × 3 apples. I have 27 ÷ 3 apples. I do not have i apples. >m-muh non-constructibles Still can exist in a continuous context. There are two atoms π units apart. After e seconds, shit happens.
Bentley Ortiz
>no physical representation in the real world the fact that that was written on an AC-dependent device... fucking KEK
Carson Thomas
Complex Numbers are useful for Physics, Electrical Engineering & Mechanical Engineering.
Unlike Poetry or Philosophy.
Jaxson Lopez
>non-constructibles show me -3 apples or π apples
you would have never extended the number line past the naturals, enjoy living with your head stuck in the ground
Cooper Nguyen
>please tell me how to get this this mythical realm of yours where one can possess 7 + 9i apples. Easy. You possess 7 real apples and you imagine 9 more. :)
Henry Perez
The Schrödinger equation >the greatest formula of Modern Physics
the imaginary number [math]i[/math] appears in physics whenever waves or rotations are involved.
In this case (Schrödinger equation) the [math]i[/math] tells us that particles of matter behave also as waves (ie wave–particle duality)
A fundamental truth of universe
Luis Butler
t.brainlet never took a abstract algebra course or a complex analysis course.
Jaxson Ortiz
you have i apples. if you make a square of your apples, it'll just be a negative apple.
Thomas Murphy
Spotted the brainlet. Real maths (aka maths more complicated than just counting apples) works with structures so abstract and so disconnected from the real world so that complex numbers look like very friendly and down to earth object compared to them
Caleb Martinez
Stop, you're not proving anything. If something can't be easily and directly related to the quantity of apples then it's not real math. (Note that apples must me chosen, if you found a way to relate complex numbers to quantity of oranges or pears that still wouldn't make them real math)
Henry Jackson
Actually, you should me more suspicious about existence of reals than of complex numbers. Given reals complex numbers are just pairs of reals with fancy multiplication. But reals, they require some weird infinite processes like adjoining infinitely many roots to Q, or making equivalence classes of uncountably many Cauchy sequences. Even Wildberger accepts complex numbers (over rationals), and not reals
Jeremiah Richardson
>adjoining infinitely many roots to Q that would be a proper subset of the algebraic numbers, which in turn are a proper subset of the reals
Dedekind cuts are where it's at
Jace Ortiz
>What is a splitting field
Benjamin Sullivan
>What is the most famous result from Galois theory
Thomas Brooks
Nice joke mate >think complex analysis is useless Haven't you worked with physics before idiot?
Lincoln Myers
I don't know, what is it?
Gabriel Garcia
If you want to find 3th degree polynomial roots then you're forced to use imaginary numbers even if you polynomial or your roots don't contain an imaginary term
Parker Robinson
For a sec I thought you meant radicals (nth roots). Algebraic numbers can't always be represented by these
Algebraics are still a proper subset of the reals
Kevin Scott
>literally no physical representation in the real world not true
Ryan Smith
They work perfectly well in our system of mathematics and have led to discoveries applicable in the real world despite not being "real" themselves. What's the problem?
Ethan Johnson
They represent coordinates so of course saying things like (0, 1) apples and (0, 1) metres doesn't makes you stupid nonce.
Elijah Edwards
>The numbers are called imaginary therefore they must be made up Literally fucking retarded
Joshua Brooks
>And before retards start coming in to debate this, please tell me how to get this this mythical realm of yours where one can possess 7 + 9i apples. Please tell me how one can possess -7 apples. Please tell me how one can possess 2.15 apples. Please tell me how one can possess [math]\sqrt{2}[/math] apples. Please tell me how one can possess 10^100 apples. Please tell me how one can possess x apples where [math]x^2+1=0[/math].
Brayden Jackson
en.wikipedia.org/wiki/Quaternion It's like complex numbers, but there are three distinct complex complex terms and multiplication doesn't commute. My friend who did game design said they used them sometimes for moving and rotating bodies in 3D.
Levi Garcia
That is literally all of math. You can not quantify anything in the real world correctly with math a human could understand.
Mason Cooper
yeah I remember that from last night, I think they tied it into Jews somehow too
Ian Thomas
>you can't have apple debt or cut apples into fractions
Lincoln Phillips
I can show you three apples, two of which are an arbitrary distance from each other, and the third is π times that distance from the first. I can also line a bunch of apples up on an axis:
Apple 1 ---- Apple 2 ------ Apple 3
And say that apple 1's position relative to apple 3's to apple 2's position is a negative number. All ratios and fractions can be represented with 3 positions as well.
However, you cannot represent i this way, because it is fake math.
Ryan Morris
no two apples are exactly the same therefore it's impossible to have two in a non-abstract sense
Josiah Harris
>A fundamental truth of universe no such thing. All truths are transient.
Elijah Morales
I guess since -1 apples can't exist, negative numbers are useless either.
Chase Howard
>doesn't know how to phase shift apples. Why are you such a brainlette op?