Complex numbers are worthless

i can show you any real number represented in apples, or as an infinite series of apples.
can you show me "i" apples "i" times?

There's a point where concepts in math stop being tied directly to what is sensible naturally and start being accepted because they're self-consistent and useful. All that is required in mathematics is logical consistency, not pretty pictures or a relationship with apples. The sooner you realize that math can go beyond reality, and that it can be incredibly useful to do so, the sooner you will level up in math.

>if i can't visualize it, it's not real math!!!!

thanks for telling me what i already know brainlet... im an EE bachelor -_-
you need to grow up and realize that this could all be replaced with real values instead of garbage like root -1, this is abstraction for the sake of it and nothing more than masturbation

look at physics, "dark matter", "dark energy", "em drive" -- all could be replaced with new theory that fits more but people like you are just jerking off about it too hard to figure that out.
pic related, its you

They're no more "made up" than zero or negative numbers. Complex numbers are essential to our understanding of mathematics and physics.

Lots of math is interconnected. I'm interested in various interpretations, not just "the algebra checks out".

>Doesn't like abstraction
>Calls people a brainlet
I can see why you're only in EE.

now thats a good argument

>not understanding complex numbers

Pleb detected

>hur hur 7 is prime because we invented it to be prime

leave

what is -1/12 apple

you can achieve this using subtraction, which is defined as negative addition of apples :

alas, remove 1/12 of an apple and therefore you have conjured a virtual " negative " apple

I don't know if you're being intentionally obtuse or you're just actively ignorant of these areas you're criticizing. Complex numbers were invented to aid in the solution of algebraic equations and it turned out they're useful as fuck for modeling reality in various ways too. Just because you can represent a complex number, their addition, and their multiplication, as a pair of reals because they make you more comfortable, doesn't mean they're a 'useless abstraction'. They're quite obviously a useful as fuck abstraction, used widely in physics, and it's much less likely that they would've been discovered had people not had the balls to try and see this square root of -1 idea through.

As for the physics that you're criticizing, you're being one of these people right now

explainxkcd.com/wiki/images/6/6d/astrophysics.png

If you think astrophysicists whose job it is to think about this shit as much as you think about EE haven't thought about your thoughts on their field, you'd be extremely wrong. Their job is to rule every possibilitiy out, turns out dark matter fits things the best still. Until you come up with a better model (which many people smarter than either of us are trying and failing to) then there's little to say other than 'dark matter is the best hypothesis to fit the data'. If you want to go against that then you're just going against the scientific method at this point.

The emdrive is bullshit btw and harold white is a scam-artist whose methods are extremely questionable.

>i can show you any real number represented in apples
No you most certainly can fucking not. Even 1/2 of an apple is impossible to produce.

For one, the notion of a discrete "object" that has definitive properties is an abstraction from physics, it doesn't even describe the real world. Even then, the mass of an object comes in discrete mass units, atoms, do you really think you're capable of dividing an apple into exactly 1/2 of itself by weight, down to the atom?

Which leads to another problem, an apple is a finite collection of atoms. Real numbers allow infinite divisions; for instance rationals are dense in the real numbers. Even if you split an apple to it's most basic parts, you'll never produce an infinite amount of divisions.

Don't even get me started on the feasibility of irrational divisions of a physical object

Taking an object in reality and looking at it numerically is 100% an unrealistic, mistake-ridden and assumption-ridden process. It happens to be a very good MODEL, but bears absolutely no absolute, truthful correlation to what we see in reality.

any rational or irrational number N under 1 can be represented by simply saying that one apple is 1/N of N apples
why would you think we need infinite divisions? too much math brainwashing ruined your common sense buddy boy.

>apple can only be divided finite times

I don't think you understand what this means. You can get some division "sort of equal to" 1/e, but you cannot get 1/e since it is irrational. Even rationals are mostly impossible because most primes do not divide a number.

Show me .0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 of an apple.
You can't because that's too small a division of an apple. Also you're retarded.

e apples would be 2 apples + 1/2 apple + 1/6 apple + 1/24 apple to infinity
division been previously discussed.

thats easy to show as i previously said, this would be the amount of apple that fits in one apple 10^175 times

you guys just refuse anything that your brainless TA or crazy professor didnt tell you, just like how you reject wildberger when he is 100% correct about everything he says.

>Acolyte of Wildberger
>believes in e as an 'infinite' sum

You are definitely trolling. gg m8 had me gigglin

Also, how bout those dark numbers?
youtube.com/watch?v=nK6XawDE8_U&t=2m30s
Those are like dark matter, right?

yeah so what? its just a name man.

>EE
>Says i is garbage
>Literally used everywhere in capacitors and circuits

k.

quality b8

It's a joke about how the sum of 1+2+3+4+5+... =-1/12

>Likewise you can show me 1 apple, or 2 pears, but you can't show me 1. It's an abstract concept, and it's something that humans generations ago struggled to even accept as a lone concept.
[citation needed]
You're saying that before mathematics they didn't have the word *one* or *nothing* in their vocabulary.
Yeah, sure.

>not infinite matter in the universe
>wants to represent a number with an infinite series of finite matter

ok... you got a stroke lately?

>No you most certainly can fucking not. Even 1/2 of an apple is impossible to produce.
How much of a retard one has to be?
Have you ever tried cutting an apple in half?

define """""half"""""

Oh, whoops: you just tried to define 1/2 (a half) by using a half.

What is a woppbebop?
A big zapusabob
And what is a zapusabob?
A small woppbebop!

THIS IS THE LEVEL OF LOGIC THIS FAGGOT HAS

>Even 1/2 of an apple is impossible to produce
[math]1/2=[(1,2)]\in \mathbb{Q}[/math].
Therefore [math]1[/math] green apple and two red apples.
But the decimal expansion of [math]1/2[/math] is [math]0,5[/math].
Hence [math]5[/math] yellow apples.

* [math]1/2\in [(1,2)]\in \mathbb{Q}[/math].

>Oh, whoops: you just tried to define 1/2 (a half) by using a half.
But 1/2 is literally a half.
By solving 2*x=1 for x you define the division 1/2.
Get off the meds.

Okay, agreed

1/2 is a half.

Now what is a half?

He's saying there was a word for one, but they would have trouble understanding the concept of "one" independent of an object you retard. They understand 1 apple + 2 apples = 3 apples, but if you just say 1+2=3, they'll ask "3 what?"

proof that human beings are not ready for complex analysis and it needs to be remodeled

>He's saying there was a word for one, but they would have trouble understanding the concept of "one" independent of an object you retard. They understand 1 apple + 2 apples = 3 apples, but if you just say 1+2=3, they'll ask "3 what?"
That's (You)r and his assumption.
How the hell do you even know that?

>Now what is a half?
You take an apple and cut it in two seemingly equal parts.
Each part is a half.

I remember reading about some guy traveling Siberia in the 19th century trying to explain the people there logic. Talking about abstract objects is a surprisingly alien idea to people who never did anything but feeding their family's mouths. If I remember correctly it was something like "Polar bears live where there's a lot of ice. There is a lot of ice at the north pole. Do polar bears live at the north pole?" and the Siberians legitimately could not answer that questions. They would respond stuff like "How the hell would I know? I've never seen a polar bear and I've never been to the north pole! How would I know?".

>They would respond stuff like [...]
That's because they're retarded.
Try asking that to any brainlet.
The correct answer is that you can't infer that polar bears live in the north pole from the two previous statements.
>But guys, a guy traveling to Siberia said that hence I'll report here verbatim.
Seriously.

why are you saying they're retarded then saying that the answer they literally said was right? maybe accept that your 2 gpa math degree doesn't mean that you're the only one who can think in the world faggot.

Who gives a shit. Natural numbers are still an abstract concept. If you think differently you are officially retarded.

>why are you saying they're retarded then saying that the answer they literally said was right?
Explain me what does
even mean then.
The travelers is saying that
>Siberians legitimately could not answer that questions.
so
>They would respond stuff like [...]
What we understand from this is that whatever the answer, they did not get the logic of it.
Try asking that to a random person in a civilized country and you'll get the same dumb reaction.

>What we understand from this is that whatever the answer, they did not get the logic of it.
baseless assumption, not necessarily true. leave my thread immediately

That's the conclusion of the traveler, not mine.
Prove that *they get the logic of it* based on the story posed above.
You can't.

>prove does/doesnt exist you cant

"half" in common language and "1/2" in rigorous mathematical language are very different things.

>Count apples using marks.
>Count days using marks.
>Count fishes using marks.
>Make up = sign for II and Y sign for III to save space on my wooden stick.
>Used to mark Y when having = and I objects.
How are marks on a stick an abstract concept?

If a half is 1/2, then it's impossible to cut things in half. You can cut things to about 1/2, but never exactly 1/2.

If we're talking about the relationship to rigorous number systems to reality, this is not pedantry, it's a very important distinction. Exact 1/2s don't exist in reality.

>physicists created dark matter in order to explain something

IT WERKS.. BUT...

>physicists cannot explain dark matter fully

OH SHIEET

is that thom yorke

>literally everything you sense is filtered by your a priori faculties

You can't even begin processing what "marks" are without structure existing in your brain to do so, that structure is the origin of counting numbers.

It's just an unfortunate naming convention. Imaginary numbers are no more "imaginary" than negative numbers. If you can't understand a result in that number system, that doesn't mean that the number system is worthless.
It means that YOU are worthless.

>You can't even begin processing what "[apples]" are without structure existing in your brain to do so, that structure is the origin of counting numbers.
Therefore apples are an abstract concept.

i^i = x
e^i^i = e^x
e^i*i = e^-1 = 1/e = e^x
log(1/e) = x = -1

i^i is -1 and not 1/(e^π)^(1/2)

watch your parentheses; e^(i^i) is not (e^i)^i

Negative numbers were invented by the banking establishment so they could charge people with nothing.

You are an idiot m8

ITT retards thinking imaginary numbers are actually "imaginary" to make things right.

How do you even begin to model how a capacitor works without imaginary numbers?

>he doesn't know the a priori/a posteriori distinction
iep.utm.edu/apriori/

Time for the baby science student to get caught up in philosophy.

To answer your mockery, no, apples are not abstract, but the notion of "object" is, same with the abstract categories by which we can differentiate apples at all. This same a priori structure (NOT content) to our experience is the same place from which we derive understanding of counting numbers.

How the fuck are you an EE and complain about complex numbers? They should be everyday life for you.

>"im an EE bachelor"
>doesn't see the value in j

eat shit

the value isn't in "root -1." it's in the complex plane

Let [math] e^z = i [/math] where [math] z \in \Complex [/math]. Then
[math]
i^i = (e^z)^i = e^{zi}[/math] is a possible solution for [math] i^i [/math].
[math] z := a + bi \Rightarrow e^z = e^{a+bi} = e^ae^{bi} = e^a[cos(b) + i sin(b)][/math]
[math] e^a[cos(b) + i sin(b)] = i \Rightarrow a = 0 , b = \frac{\pi}{2} + 2\pi n [/math].
So all possible values of z are [math] 0 + (\frac{\pi}{2} + 2 \pi n)*i [/math]
Therefore [math] i^i = e^{((\frac{\pi}{2} + 2 \pi n)*i)*i} = e^{-(\frac{\pi}{2} + 2 \pi n)} [/math]

Are numbers just a meme?

I told you to define half and in your definition you used the word half.

The correct answer is "maybe" so those are all literally the correct answers

A half is when you divide an arbitrary amount in two equal parys

Not this cancer again

You can't visualize R^4 vector space either

What a fucking retard.

Okay, nice definition.

Take the result of the banach paradox.

You can take a set, and then turn it into two equal sets, that are themselves equal to the first set.

So 1 = 1/2

GOT IT BRO
YES

Do you even know what that is or did you just watch the vsauce video and now you're an expert on math?

10 year old autist detected

Math=/=science

Math can go beyond the limits of reality if it makes sense mathematically. Like imaginary numbers.

Uh sure bro

what if I cut a banana into two equal parts? what are those? they can't be a half, because only two equal parts of an apple can be a half.

so.. if you cut a banana as above, do you get two halves of a banana? and before, you got two halves of an apple?

so, then, what is an intensive definition of a half? how do I know a half when I see one? how can I generate new types of half?

you don't mean "reality", you mean "sensory perception". or "common sense", which is a crude evolutionary heuristic. mathematics less crude, but still undoubtedly a heuristic

Youre missing the point man, everything exists as a singular category of being.

An half an apple is in the category of "half apples." Not "Apples."

They dont serve the same function and dont have the same properties. You cant have one half of an "Apple", as thats categorically different than "Half apple"

give them potato wine

start by trying to visualize e^(theta*i). (It traces out the unit circle in the complex plane)

still with us brainlet? ok good

i=e^(pi/2*i) and take both sides to the power of i.

Get rid of your fake notion that numbers represent the number of apples you have, it's a horribly misinformed way of teaching mathematics which breaks down in grade 2. Explain to me what -1 apples -1 times means.

Complex numbers are just 2d numbers. Get used to it or stop trying to wrap your dumb brain around these not so complicated concepts.

>i^i visualized?

That's because the number of apples is a linear relationship hence can be described using the real line. It seems like you don't even understand the basics of what complex numbers represent.

surprise, infinity =/= big number

[math] \displaystyle
i=e^{\frac{\pi }{2}i}
\\
\displaystyle
i^i=({e^{\frac{\pi }{2}i}})^i=e^{-{\frac{\pi }{2}}} = \frac{1}{e^{\frac{\pi }{2}}} \approx 0.2787957
[/math]

That's just one of infinitely many results

Derivatives, wich apply to nonharmonic waveforms aswell.

Matter of fact, you don't need complex notation, just like you don't need quadruples to describe Maxwell's theory. It just happens to extremely simplify the description of harmonic waveforms and signal theory.

You retarded autist

Describe an object you see.
The result of your description is *abstract*.
Therefore the apple is abstract.
But the apple is not abstract.
The make the same reasoning for *a half*.
We see halves everywhere.
You have a point by saying that a half, like an apple, is both abstract and non abstract.

>Youre [sic] missing the point man
>Your point of view differs from the one I've been taught man

Halves are as tangible as apples.
Deal with it.
Think hard about this and about what differentiates halves with apples.

>with
* from.