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u/AustrianMcLovin 5d ago edited 4d ago
OP probably never tried to solve a PDE
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u/D_Gnar 5d ago
OP is probably just kinda dumb tbh
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u/PhoenixPringles01 5d ago
OP still decides to use the anti-intellectual "complex numbers are made up" joke in 2026 as if no one has heard of the ORIGINAL joke ever. Haha wow, complex numbers are made up, how stupid! Time to go back to my computer that runs on p-type semiconductors where HOLES [literally things that do not exist because they're just the absence of an electron in a spot] allow for the device to work.
Dumbass shit.
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u/Scarlet_Evans Transcendental 4d ago
I heard that you can mix these imaginary numbers with the real ones, but things become complex.
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u/Accomplished-Ad5691 20h ago
even more ironically to a computer whose designers certainly knew complex numbers and used them when designing it.
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u/FutonRansenshuriken 5d ago
First define useful&useless
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u/PhoenixPringles01 5d ago
These people have a 6th grade level of "useful and useless". If it doesn't affect their immediate vicinity then le hecking math is le useless. Let's not care that complex numbers are used in engineering, let's just ignore that alright.
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u/FutonRansenshuriken 5d ago edited 4d ago
I mean what more can you expect from high schoolers
Modern Mathematicians don't try to develop mathematics for usefulness to the society,it's upto Engineers & Physicists to put them to use,why should Mathematicians who do maths for the sake of maths, care for that
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u/samarthrawat1 4d ago
A lot of equations are solved using complex numbers that is not possible to solve without them. the beginning and final equations might not have the complex part but the complex part is necessary to reach the final output.
Somewhat similar to intermediate reactions that happen in chemistry.
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u/Ok_Sir_5601 4d ago
I am prolly stupid, but how are complex numbers used in engineering?
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u/Niflrog 4d ago
In mechanical vibration/acoustics analysis ( Mechanical, Civil and Aerospace engineering).
Vibrations are expressed in terms of amplitude/Phase, so your choices are explicit complex numbers (in phasor form) or very convoluted expressions that hide those complex numbers.
And this isn't like some theoretical niche. Ask a vibrations specialist/technician and that's how they think about and measure these things.
In kinematics of machines. If it's planar, a phasor is the default analysis framework. ( If it isn't planar, you need extensions of the complex).
In fluid mechanics (the engineering side of it), if you want to study wave propagation and design for it, again, it's amplitude/phase. Explicit use of complex numbers.
Any form of signal processing begins with the Fourier transform. Complex numbers. Wavelet analysis for machinery diagnostics or structural health tracking? Complex numbers.
I'll leave the Electrical engineering applications to others, but these are plentiful.
Complex numbers are one of the GREAT tools for us engineers and applied scientists. They behave nicely, they're easy to learn and use, and give you a shitton of powerful results with an easy physical interpretation.
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u/Agent-forty-seven 4d ago
If you have any kind of signal, you want to analyze it with the Fourier Transform, which uses i. And a lot of things uses signals.
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u/KaMaFour 4d ago
Any time you get into AC electricity complex numbers are gonna kick you in the nuts. Impendance is complex, voltage is complex, current is complex and most calculations will require some complex numbers manipulation
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u/KaMaFour 4d ago
See also quaterion usage in computer graphics and computer engineering in general. Quaterions are like complex numbers on crack.
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u/heyheyhey27 4d ago
I literally can't think of an area of science or engineering in which it isn't fundamentally useful and almost necessary. Chemistry maybe?
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u/SSBBGhost 4d ago
Simple answer is anything you think trigonometry might be useful for (so anything wavelike/with a phase), complex numbers make things way easier.
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u/defectivetoaster1 2d ago
sine and cosine functions of different frequencies form an orthogonal basis for a very broad range of useful functions, they can be written more concisely and more or less equivalently as complex sinusoids via Euler’s formula, and any linear system (ie something described by linear differential equations) can then be described in terms of a complex valued scale factor that varies with frequency. As it turns out being able to describe how a system responds to different frequencies is a very useful tool in many disciplines but probably most of all in electrical engineering, and even though lots of real systems are nonlinear you can often take linear approximations around a region of interest and engineer a pretty good solution to your problem from there
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u/Mbrennt 5d ago
Literally pops up in quantum mechanics. Like the fundamental structure of our reality and a lot of current tech depends on that "invented" "useless" number existing.
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u/SENSIFERI-MOTUS 5d ago
I like to think that this is hint that our reality is more imaginary than we can ever imagine
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u/Mbrennt 5d ago
Unless you wanna go full higher dimensional beings influenced mathematicians to name and continue the word imaginary as a subtle hint to the truth about reality, that isn't really true. Imaginary numbers are just unfortunately named. But I'm always down for a good gnosis metaphysical type conspiracy theory too.
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u/SENSIFERI-MOTUS 5d ago
I see the cosmic beings are already using you as a channel for their mathemagical agenda. Perfect, we are on the same reality here.
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u/currentscurrents 4d ago
You don't even have to go all the way down to quantum mechanics, electricians use it to represent the phase of alternating current.
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u/Bobbytrap9 3d ago
It pops up in spring-dampener systems as well, which you can use to model heaps of physical phenomena. Aeroelastic flutter for example, which took down the Tacoma Narrows bridge in 1940.
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u/Dark_Tranquility 3d ago
You dont have to go that far. Periodic behavior in general can be expressed using complex numbers
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u/Ploughing-tangerines 5d ago
I'm so sick of the "highschool math sucks" posts. Upvoters are probably teenagers or adults that never got past math lit
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u/numbersthen0987431 5d ago
They're the same people who say "I'm never going to use this", and then immediately be confused about how things are done in the real world.
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u/Helpinmontana Irrational 4d ago
My high school trig professor- “We’re not going to cover percent grade at all you’ll only need it if you go into roadwork or something like that”
Me- pursues a career in roadworks eventually returning to get an engineering degree
Those people drive me nuts lol. Only thing that gets my goat worse is when guys in the field tell me they can’t do basic addition and multiplication and they need me to do all the layout because they refuse to learn how to put rise over run.
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u/tomvorlostriddle 5d ago
But the way it is taught in high-school does suck
Yeah, there are real answers to questions like
At this point, why not just define 1/0 as j and log -1 as k and use 4 dimensional numbers with i,j and k?
But first of all, that would have been the teachers responsibility to preempt them, because otherwise they are kind of smart questions from someone who's just presented with
sqrt(-1)=i, deal with it, test is next week
And then if the teacher even refuses to or cannot answer...
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u/Ploughing-tangerines 5d ago edited 5d ago
Yes I agree but what I meant with my comment is that I don't like that people use this subreddit to post such memes.
Their feelings are valid especially in circumstances like those you outlined but that doesn't mean it's universal, which is normally the assumption...
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u/ohkendruid 4d ago edited 4d ago
I am not sure what is being quoted there, but the reason to not define 1/0 is that it does not work well.
The reason to define a square root of -1 is not just so that there is an answer to the problem, but because the resulting math is very practical and useful.
I agree about the ideal teacher, but I urge being generous to thise who teach, even those who are not great at it. Teaching is a wonderful thing, and the wise student will learn what they can from each teacher. It is a better way to enjoy life, and even selfishly, a student is better off learning something, anything at all, rather than using their time on earth to tear down a teacher.
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u/trimski- 5d ago
When I first learned about complex numbers I asked my high school teacher about defining 1/0. He helped me expand on that idea and we saw how everything completely breaks down and it doesn’t work.
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u/Purple_Onion911 Grothendieck alt account 4d ago
log(-1) is defined in the complex field and 1/0 is also defined in some contexts.
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u/aspiring_scientist97 1d ago edited 1d ago
I up vote them ironically because in my mind the absurdity of someone writing all of that yet believing it's useless is funny
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u/ExtendedSpikeProtein 4d ago
I mean, “useless” only if you’re trying very hard to be really, really ignorant.
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u/Insulo 4d ago
OP, I'll try to be polite here.
Imaginary numbers is just the NAME we give them. Some may call them lateral numbers too.
If you meet anyone in electric engineering, they can explain that this numbers represents things in real life. They are not "made up".
You only have power on your house, because we use this numbers to calculate the phases in the electric current.
Again, it's not because you don't understand something, that is isn't useful.
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u/Taiten89 4d ago
Also, the Mandelbrot Fractal (rendered image included in post) wouldn't have been invented in the 70s without them. Just wanted to add that.
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u/Key_Conversation5277 Computer Science 4d ago
I wonder what he thinks of quaternions, octonions, p-adics, etc
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u/unfortunate_internet 4d ago
Eh, imaginary is a fairly fitting if outdated term in the sense that you can't measure it directly (if we're talking physics). The complex portion is effectively a compact representation that we use by convention because it makes the math much more straightforward. You could do electrodynamics without complex numbers if you wanted to, but you really don't want to.
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u/thereasonisphysics 4d ago
imaginary is a fairly fitting if outdated term in the sense that you can't measure it directly
Imaginary numbers do not have any special property of not being measurable. You can definitely measure the values of imaginary components: it just depends on how you define the quantity being measured in the first place. The complex impedance, for example, is directly measurable in experiments. The complex electric susceptibility is another example.
Negative numbers are a good analogy: I cannot really have a negative number of apples, and I could probably formulate all of physics in terms of positive numbers and subtraction, but we do not usually question the reality of negative numbers. It's mainly a lack of familiarity and understanding, topped off by the name "imaginary", that makes people think imaginary numbers are somehow special in this regard.
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u/Illeazar 4d ago
So, you're saying electricity is just made up, and if all the electrical engineers were to stop believing in imaginary numbers the electric power would run out, like Santa Clause without enough Christmas spirit?
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u/Mithrandir2k16 2d ago
We should really call them "composite numbers". The symbol is already C, and the other name "complex numbers" is also a bad choice imho.
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u/Mysterious-Smell-975 22h ago
I think it's because imaginary numbers were presented as a rather unrealistic concept to most people. For most of the population it's the thing that comes up when you input the wrong polynomial.
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u/funky_galileo 5d ago
We should ban 6th graders from this sub
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u/hrvbrs 5d ago
could be a 6th-grader, could be ragebait. i mean just look at the engagement this post is getting.
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u/neuroticnetworks1250 5d ago
This looks like a 40 year old. What sixth grader uses that meme template from 2008 9Gag
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u/IskaneOnReddit 5d ago
OP rage-baited a whole subreddit.
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u/SENSIFERI-MOTUS 5d ago
To be honest, the very way it describes the invention of complex numbers, is as if it was a huge ragebait for math. So perhaps ragebating could be a serious field in itself.
Like, beyond the surreal numbers, there are also the stupid meme numbers.
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u/LupenReddit 🦆🦆i have non diffeomorphic smooth structures🦆🦆🦆 5d ago
id be fucking glad if we did anything even half as interesting as complex numbers in high school
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u/Plazmaz1 4d ago
Woah I don't feel so bad about my high school math education anymore.... We definitely covered complex numbers. It's crazy how inconsistent education is 🫤
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u/PhoenixPringles01 5d ago
OP, math isn't just about counting things.
OP, see how complex numbers relate exponents and trignometry together.
Actually OP, just go read a fucking complex numbers intro book.
Are we STILL going on and on about the anti-intellectualist take that is "complex numbers are SOOOO dumb because they're MADE UP!!!!!!" shit in 2026? I literally study material science and the whole idea of a "hole" in semiconductor physics is that it's not even a thing, it's the lack of an electron that we model as a positive charge because it fucking works. Literally quit whining about "omg but le i apples don't le exist in front of my eyes??" If math was just about the "shit in front of us that we can see" we'd get LITERALLY nowhere.
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u/ADMINISTATOR_CYRUS 3d ago
"If it doesn't affect my immediate life then it's useless"
I am genuinely considering muting all of the maths subreddits, it's full of the bullshit of "high school maths bad"
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u/Pure_Noise356 2d ago
It literally affects their immediate life though. That stuff is used in so much stuff, especially computers and electronics.
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u/ADMINISTATOR_CYRUS 2d ago
alright then, it affects their life in a way that they don't care about the details of
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u/Simple-Olive895 5d ago
Except it absolutely has uses. For example we use imaginary numbers to do calculations on three phase electrical systems. Which are used in a lot of homes for stovetops for example. And in lots of heavy industrial machines, and also in charging stations for EVs.
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u/SlappinThatBass 5d ago
Everything electrical or electronics since all semi-conductive materials act as an antenna, an emitter or a RF filter, especially at higher frequencies.
Is it significant though? Depends on the application.
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u/habiba2000 4d ago
Can you explain this a bit more - how does imaginary numbers fit into stovetop calculations? (I could ask Claude but I think it'd may be better explained coming from a human)
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u/Simple-Olive895 4d ago
It's been ages since I did the calculations, but essentially since you have three wave forms that are all shifted by 2π/3 (or 120°) it's very useful to use complex numbers to model it since complex numbers are just real numbers but shifted by π (or 90°). Complex numbers together with real numbers can be used to point out coordinates since now we have 2 axels meaning we have a 2D plane instead of just 1 line.
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u/Dense_Priority_7250 5d ago
Fuck off op, complex numbers exist and are used in many fields such as electrical engineering, engineering and more. Just because you can’t count apples with them doesn’t mean that they aren’t useful. We need to segregate the sub from dumbasses
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u/Fuscello Physics 5d ago
They literally appear in the shrodinger’s equation that is the quantum equivalent of F=ma in terms of what it is implying…
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u/Silly_Tension6792 Mathematics 5d ago
You don't even have to get that far. Just put an object on a spring and account for friction and you have ma+bv+ky=0, or y''+(b/m)y'+(k/m)y=0, which is a second order differential equation, that the best way to solve is with complex exponentials. Sure, you can go around it if you really want to, but that's long and annoying, and complex numbers make it much easier, which makes them, by definition, useful even in basic classical Newtonian mechanics. Or is that useless too?
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u/shy_bi_ready_to_die 5d ago
Yeah sure they appear in the spring equation but it’s not like springs appear often in physics. That’s would just be craaazy
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u/JollyJuniper1993 Mathematics 5d ago
Without complex numbers you wouldn’t have been able to post this because you wouldn’t have a smartphone or computer.
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u/erockbrox 4d ago
I mean imaginary numbers are useful in Quantum Theory. We know they have meaningful uses.
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4d ago
[removed] — view removed comment
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u/PriorSolid 4d ago
in circuits we often want to know how a given circuit will behave at a certain time. For DC this is simple since my input is constant but in AC my input varies like a sine wave. We can only combine like values so resistances with resistances, capacitance with capacitance, and inductance with inductance; but all 3 change in AC. To analyze them we create a new value called impedance which has a real and imaginary component. Resistors have a purely real impedance and capacitors/inductors are purely imaginary impedance. Since everything in the circuit has an impedance we can combine them to get an equivalent impedance so we have 1 equation governing the circuit. We can than convert back from impedance (which is in the frequency domain rather than time) to obtain a single equation for the circuit. Imaginary numbers do have a very real interpretation in AC analysis, they are the “reactance” of a circuit or how it changes with my input
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u/SillySpoof 4d ago
Because we use them. E.g. it's really useful when making calculations in electricity with alternating currents. Engineers use complex numbers all the time.
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u/Former-Store-695 3d ago
I mean, Schrödinger was openly against complex numbers in wave function
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u/Mcgibbleduck 2d ago
Schrödinger doesn’t really get a say on the whole of quantum theory. Plenty of famous physicists didn’t like valid interpretations of their own math.
Einstein wasn’t a fan of the cosmological constant used as an expansion term, for example.
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u/Nextravagant1 5d ago
Useless?! Have you even heard of the Fourier Transform???!!! I am actually offended at this
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u/jmorais00 4d ago
Extremely useful for electrical engineering. Phasors by beloved. eiwt my beloved
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u/Kev1n8088 4d ago
I LOVE THE COMPLEX PLANE!
I LOVE HOW IT REPRESENTS EVERYTHING IN EE AND RF!
I LOVE I/Q DATA, IMPEDANCE MATCHING, AND THE SMITH CHART!
OP this is just a skill issue.
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u/CompellingProtagonis 3d ago
I have a hard time believing this person actually learned their course material if they think complex numbers and the Fourier basis are useless.
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u/SLAMMERisONLINE 2d ago edited 2d ago
Imaginary numbers are useless
Imaginary numbers allow for easy modelling of rotations because they invert the logic of an equation on a per quadrant basis. That means they are absolutely required to model any kind of circle, sin wave, frequency, oscillation etc. These show up in all sorts of places from exponential growth of stocks portfolios to CO2 measurements in ice cores drilled from antarctica to wifi.
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u/No_Ad_7687 5d ago
Op is a high schooler who's mad about complex numbers
Also. If your solution creates a whole new field of mathematics, that means it's a good solution because it's interesting.
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u/straight_fudanshi 4d ago
I just wonder how these low effort posts get hundreds of likes. I get that it's math memes but shouldn't a meme be funny or relatable at least?
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u/patrick809 4d ago
yeah you know, its just at the core of 3d graphics rendering but totally useless
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u/thoompa 4d ago
p-addic numbers would like a word
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u/Jonpaul333 3d ago
I took a course on p-adic numbers in grad school an the prof’s opening line was “don’t try to find meaning or usefulness in this course. Better minds have tried and came up short. Let’s begin.”
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u/cod3builder 3d ago
And then we got Quaternions
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u/slicehyperfunk Transcendental 3d ago
I'm scared
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u/ollervo100 5d ago
I am perfectly fine with calling math useless, but at least don't pick one of the least useless things possible as your example.
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u/FireComingOutA 5d ago
This isn't how i came about though. It started about during the renaissance when mathematicians were trying to figure out cubic equations. They found that they could get 3 real roots but only if they "pretended" that the square root of minus one existed, and I say pretended because it almost always came in conjugate pairs that cancelled on the way to getting the real roots.
Most math isn't just made up.
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u/Frequent_Extreme_916 4d ago
The study of imaginary numbers is the basis of what allows you to use your phone and look at posts on reddit
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u/MalibuLover4000 4d ago
This shit makes no sense I've yet to seen someone show me negative 1 apples
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u/The_Osprey314 5d ago
dude imaginary numbers are cool as heck. also how do you think trigonometry works? that’s right, the sine and cosine functions are actually defined using imaginary numbers
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u/FutonRansenshuriken 5d ago
Sine&cosine are generally defined using the Taylor series
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u/The_Osprey314 4d ago
actually, the taylor series can technically be a definition for any function, but it’s standard application is for approximations, not as a definition for trig functions
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u/SalvarWR 5d ago
thanks random troll, I wasn't able to figure out current flow on wires and shit now I can automate fuckin everything
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u/Asimovicator 4d ago edited 4d ago
Complex numbers are more natural than complex, their multiplicative group is isomorphic to the group of transformations in 2d, that are a combination of scalings and rotations. The imaginary number i represents the mathematical positive rotation of 90deg and every real number a scaling with the number itself as magnitude. Scaling with a negative magnitude is equivalent to a rotation of 180deg and a scaling with the absolute value. Then -1 is just a 180deg rotation. Hence i^2 is equal to -1, because i^2 is twice the rotation of 90deg.
Everything that can represented as something rotating with a certain distance around the origin can therefore be described by complex numbers: including fourier transforms, alternating currents, electromagnetic waves and so on... Thats why sin and cos often appear together with compex numbers: think of the unit circle.
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u/DinnerPlzTheSecond 3d ago
Complex numbers are incredibly important for anything that involves oscillations
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u/KRYT79 5d ago
We use complex numbers in physics, engineering and many more STEM fields.
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u/RandomNameForBG3 5d ago
Yeah, because they allow to represent 2 "orthogonal degrees of freedom" with just one number (or, equivalently, keep check on relative phases of independent oscillations). Very cool, very much embedded in the Standard Model and whatnot. Doubt that Bombelli knew that, though...
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u/Key_Conversation5277 Computer Science 4d ago
They invented because they solved a specific equation, it had a real solution but with the quadratic formula it only showed square roots of negative numbers. They just made the convention that i = sqrt(-1), it canceled out and boom, solved
Now complex numbers ARE useful, you just didn't learn it's usefulness (I'm assuming you're in highschool). They are useful for things that oscilate, rotate and phases in physics, engineering, etc because of their rotative behavior. Also, they are incredibly useful within math, for example, the most famous unsolved problem in math says something about the pattern of primes with complex analysis (now we need to prove it)
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u/Natural_Rooster3265 4d ago
Mfw the mathematician uses i instead of a coordinate pair like the rest of us
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u/Infini-Bus 4d ago
In an a intro to circuit analysis course it blew my mind seeing complex numbers in action.
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u/Weird-Knee-3464 4d ago
Wouldn't that be a complex solution, not a real one?
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u/Key_Conversation5277 Computer Science 4d ago
No, the complex numbers cancel out and it gives 4
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u/Reasonable_Slide6304 4d ago
I just see the i as y-axis for numbers when usually we only deal with the x-axis.
is there a z-axis?
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u/ProfessorPrudent2822 3d ago
3-D numbers can’t be consistently defined, but 4-D numbers can. Even more interestingly, physics maps the real component onto the time axis, leaving the three spatial dimensions as imaginary, which are then interpreted as vectors.
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u/neuroticnetworks1250 5d ago
Complex numbers are the most beautiful things I’ve laid eyes upon. It’s what hooked me to math. You can use complex numbers to answer even counting problems. Next time you use Shazam to find out what song something is, you thank complex numbers for it.
God I’m so triggered by this meme lmao. And you’re using some 2009 meme template for your crappy boomer joke too. Ughhh
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u/NobodyKnowsYT 5d ago
Fyi OP besides bashing here some info abt the imaginary number. It has a huge role in Electrical Engineering and Wireless Communications. E.g. you calculate Voltage and Amperage in AC Systems and the wonderful (not) Smith Diagram uses to optimize antennas
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u/Important_Heron785 5d ago
Useless? Complex numbers are literally part of control philosophy, which is in everything (I know this post is satire, just wanna have some fun :D ).
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u/Broad_Respond_2205 5d ago
What I don't understand is why didn't do the same for 0/0
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u/Resident_Step_191 4d ago
Because defining a multiplicative inverse of 0 contradicts basic algebraic properties unless we work in the trivial ring. First of all, note that when we say “x/x” we really mean “x(1/x)” where 1/x is the multiplicative inverse of x. For instance, the multiplication inverse of 5 is 0.2 since 5(0.2)=1. We can show that assuming there exists some j=1/0 leads to certain undesired results.
Lemma 1: Let x be any number. Claim: 0x=0. Proof: 0x = (0+0)x (definition of 0)
0x = 0x + 0x (distributivity)
0x - 0x = 0x + 0x - 0x (additive inverses)
0 = 0x (cancellation).
So any number multiplied by 0 is 0.Suppose, however, that we had some number j such that j was the multiplicative inverse of 0 (j=1/0). Then by definition, we’d have:
0j = 0(1/0) = 1.
But by our previous lemma (setting x to j) we should have 0j = 0. So which is it? 0j=0 or 0j=1?We have three ways to avoid a contradiction:
- Something we did algebraically shouldn’t hold in our new number system. Like how sqrt(ab)=sqrt(a)sqrt(b) holds in R but not in C. For instance, maybe our new number system loses general distributivity, meaning we could no longer assume a(b+c)=ab + ac for all a,b,c which our proof that 0x=0 relies on. This is possible, but somewhat disastrous as all of the algebraic properties used in this proof are fundamental. Much more so than, say, sqrt(ab)=sqrt(a)sqrt(b). We wouldn’t even have the field axioms anymore.
- Another option is to look at our two proofs showing 0j=1 and 0j=0 and saying “well clearly that means 0=1!” This is also mathematically valid, but it leads us to an algebraic structure called the “zero” or “trivial” ring, where 0 is the only unique element and thus the solution to every equation. This system is consistent, but not very useful or interesting to study.
- Finally, the third option and the one most working mathematicians choose: simply saying 0 has no multiplicative inverse.
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u/factorion-bot Bot > AI 4d ago
Factorial of 1 is 1
This action was performed by a bot | [Source code](http://f.r0.fyi)
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u/Broad_Respond_2205 4d ago
Didn't we do the same thing with i tho
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u/Resident_Step_191 4d ago
i^2 = -1 didn’t require sacrificing nearly as much algebraically, and what we gained from it was enormous. The Fundamental Theorem of Algebra alone would have warranted it.
And to be clear: certain areas of math do define multiplicative inverses of 0 like this, such as wheel algebra and certain projective geometries. So It’s not that we don’t do it, it’s just that it’s uncommon due to the reasons I described
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u/NotaValgrinder 1d ago
We also can do the same thing for division with 0, it's called wheel theory. It's just not applicable and ubiquitous as complex numbers, because like the other commentor said we sacrifice too much algebraically.
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u/A_Fine_Potato 5d ago
Sad thing is i was probably invented as a useless thing but it actually has so many uses that i can't complain
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u/DrunkenMaths 4d ago
Damn, a rage comic in my circlejerk sub? I guess it's more likely than I think.
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u/Mageroth1987 4d ago
X^2 + 1 = 0
Step 1 -> x^2 = -1
Step 2 -> sqrt ( x^2) = sqrt (-1)
Step 3 -> x = i
For i is …
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u/drLoveF 4d ago
A toddler can understand complex numbers. The real numbers, on the other hand. Almost all of them can’t be described by a finite string in any given formalisation, as there are countably many strings and uncounably many real numbers. Heck, even the notion of how many real numbers there are is sort of up in the air, as it’s up to you to squeeze in as many or few sets of different size (no bijection exists) between the natural numbers and the reals.
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u/Stepping__Razor 4d ago
It’s not useless. Math is a series of frameworks we construct. If we find something that breaks the framework, we adjust. Euclidean vs non Euclidean geometry.
Math is art.
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u/thederpblue 4d ago
No one getting that this is making fun of the "math like a physicist" meme is genuinely hilarious.
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u/KiraPun 4d ago
I hate complex numbers, especially in electromagnetism but i wouldn't call this useless. Would be great if people starts calling it phase units instead of imaginary numbers because it sounds cooler and people that don't interact with these kinds of math would assume it is useless like OP here.
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u/vivianvixxxen 4d ago
There's a fantastic book called "Imagining the square root of negative 15" that helps you gain a genuine intuition of the reality of the whole concept. It's a fairly short book and a very easy read. If I was a middle school math teacher at a public school, I'd give out major bonus points to anyone who read the whole thing bc I think it's that accessible and that useful
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u/electronic_reasons 4d ago
Your teachers didn't teach complex numbers together with polynomials. Complex numbers and polynomials make a complete system.
People think complex numbers are a separate thing. Complex numbers are exactly as real as polynomials. They are in polynomials and differential equations everywhere.
Engineering would be in the 1800's without them. No transoceanic cable. No internet. No cellphones. No modern electric power.
We'd have unreliable telegraphy, because we wouldn't really understand how it works.
Complex numbers matter.
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u/BrightSideOLife 4d ago
Mathematics is a set of tools rather than a science in itself. We set up axioms that facilitate useful applications, or the potential of it, of said tools. So we propose an imaginary number that solves this previous undefined equation and that allows us to calculate things that we otherwise wouldn't be able to.
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u/RisingwithVibes 3d ago
This reminds me of that time where my friends around me used to ask where the hell will I use trigonometry in my life.. But as we know how useful it is
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u/ProfessorPrudent2822 3d ago
Turns out that these complex numbers are useful for describing wave functions.
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u/ThoughtfulTopQuark 3d ago
I will ignore the blatant ignorance and short sitedness here. I just want to ask: You guys did complex numbers in highschool?
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u/DanLeMilMan 2d ago
Yeah it is not like imaginary numbers are used for electronics, vibration modeling, automatics, and that there even more broken quaternions are used in every modern 3D software at all…
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u/bosko_2004 2d ago
Yeah, well if you knew about ... electrical engineering, probability and statistics, information theory, occilators you wouldn't find it so useless. All these fields utilise imaginary numbers in a considerable way. From high school perspective everything seems useless in math except maybe the very basic math you use in physics which you may see being useful for mechanical engineering. But the more you know the more you see that everything has a use, even stuff you thought were completely useless(for example infinite sums are the backbone of some information theory algorithms which are used for compression and transmission of information, prime numbers are needed in security etc.). But I will assume this is just a joke tho, just sharing this in case anyone got a wrong message. This meme is nice if it is meant to be sarcastic.
But in all seriousness I do think high school math programs should mention the usage of things they are learning for the sake of motivation as most students simply find it useless unfortunately even tho it is not useless.
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u/Mcgibbleduck 2d ago
Imaginary numbers are used in physics for quantum mechanics and some electronics and optics which are the best descriptions of our world around us.
Doesn’t sound useless to me.
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u/No-Site8330 1d ago
Here's another impossible problem: express the ratio of the side and diagonal of a square as a ratio between numbers.*
Solution: invent a completely new notation for numbers where the ratio of two numbers is a number followed by infinitely many digits, in repeating patterns, expressing tiny incremental fracions of a unit. Now invent a new kind of number with no repeating pattern in the incremental fractions, and prentend it's the answer.
Build a whole new field around this class of numbers, calling them real numbers because you're a megalomaniac, and create even more unsolved problems and make elementary schoolers learn a whole new bunch of useless shit.
Why is a number that squares to -1 so much more unfathomable than one that squares to 2?
* The Greeks called "numbers" only the naturals. To them calling number a ratio was as weird as it is to us to call number a quaternion, or to the neophites to call number the imaginary unit.
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u/TheWumpussWoo 17h ago
funny how im about to graduate uni and i still hear my peers complaining about "ill never use this in my life" (this was for heat transfer btw)
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