How are imaginary numbers even possible and why are they able to be useful?

Imaginary numbers are a jewish invention to try and show that there is no such thing as truth in mathematics, that it's all subjective like morality.

imaginary numbers are by their own admission impossible and self contradictory.

there is literally no number which , when you multiply it by itself, you get -1. That's a fact.

everything real , i.e. true in mathematics that you CAN use imaginary numbers for , you can also use trigonometric functions and power series for.

I've worked as an electrical engineer for 8 years and I've never needed to use an imaginary or "complex" number.

when solving for the three real roots of

https://www.google.com/search?ei=LVAAWrOqFZDMwQKqyLog&q=y%3Dx^3-5*x%2B3

complex numbers are unavoidable

youtu.be/_qvp9a1x2UM?t=2m40s

Rafael Bombelli was not jewish. Neither were Cardano or Euler

I can wash clothes by hand, so obviously I don't need a washing machine.

Aside from that, you may not be aware of quantum physics.

>thinks imaginary numbers are some kind of vast conspiracy to make him do complicated math
>doesn't accept the jews as master race
>electrical engineer
Yep, it all checks out.

You've only given examples of things which can be described with numbers. Complex numbers can also describe things. Any mathematical concept can be used in a description.

nature is a mirror of the mathematical realm, otherwise math would be useless and the world would be unintelligible

>how are imaginary numbers even possible and why are they able to be useful?
You could call them special numbers so that they aren't imaginary and then they will be useful because they are special

They can be used to find every possible Pythagorean triple.

Why is it that right after saying something incredibly stupid, the person often adds, "and I'm an engineer"?

Work that y axis boy

In a+bi form, what is (-16)^(-16)?

I'm trying to graph the potential negative numbers of f(x)=x^x, and according to a+bi, they are either positive or negative.

What I just stated was wrong, I meant (-1/16)^(-1/16).

Dude just punch it into geogebra. That will show you the whole of the function.

botnet no thx

>how are negative numbers even possible and why are they able to be useful?
>they seem like an internal contradiction to me, based on how we define addition and substraction and shit like that...
Compare

They are in a Schrodinger wavefunction

I'm not a bot dick. It's easier to understand it when u graph it out.

Clearly he needs to see and understand the process, not just get a bunch of algebraic notation of what's happening.

>how are imaginary numbers even possible and why are they able to be useful?

How many irrational numbers do you encounter on a daily basis?

this is the way I was taught and it still makes the most intuitive sense despite the fact its not really what you are doing

...

You give hope to all the other retards out there that it doesnt matter how much of an imbecile you are, you too can be called an engineer

This guy gets it. 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.

You'll never understand how ignorant and misinformed you are, but that's okay =).

I wonder how your brain would explode when you saw complex numbers unavoidably arise from studying natural phenomena. Or if you learned how much of your everyday technology required modern mathematics to function.

>claims complex numbers appears in nature
>doesn't provide a single example
>instead attacks anyone who doubts their blind faith
Mathfags, everyone.

Literally we define a number that when you multiply it by itself, you get -1. It is called ((( i ))). Otherwise it doesn't exist.

Does we define the number √5 as the number that when you multiply it by itself, you get 5? Does we define the numer two as the number you get when you add one to one?

The whole point of imaginary (complex) numbers is that they represent a strange new idea, but /they do not lead to a contradiction/. So since they don't lead to a contradiction, we (mathematcians) choose to roll with it and see where it goes, and it ends up being interesting and useful.

Suppose two other crazy ideas: a number has such and such properties:

x is simultaneously less than zero, and greater than one.

y is some "infinitely small" thing, like 0.000...001, and is itself not equal to zero.

Both of these notions lead to contradictions, and that's why they're rejected. Imaginary numbers are weird, but not contradictory, and so they are accepted by mathematicians.

>>x is simultaneously less than zero, and greater than one.
What does this refer to?

is this the homolust thread

youtu.be/gCAxGTt7nLg?t=8m

Brain let, ultimately it's us who decides collectively what's objective or subjective. Post-modern fags are technically right but you cant throw out morality without throwing out laws and Civilization. Morality and Mathematics are 2 of the foundations that our Civilization is built on and for all intents and purposes they are absolutely objective just like the law. If you wanna be really stupid and argue semantics, the word subjective has an objective definition, and objective has subjective interpretations. Morals are subjective relative to culture in the broadest sense but for that culture to work those morals need to be objective.

Post-modern fags are just the new marxists, and subjective morality fags don't even realize they are in the same group as 3rd wave feminism.

Another thing is that imagionary numbers are just the y axis of numbers, that simple.

>I've worked as an electrical engineer for 8 years and I've never needed to use an imaginary or "complex" number.
Do you know how I know you're full of shit?
-t electrical engineer

>particle physicist here

Imaginary numbers explain a large amount of real world constants/coefficients/etc that seemingly qppear out of nowhere

pretty sure that bait friendo

That's not what OP was asking.

That's super exactly how mathematics work

Imaginary was a horrible name for them. If they had just given them some dudes name, people wouldn’t ask this question nearly as much.

Short answer: what else are we gonna call sqrt(-1) ?

It makes more sense when you get into atomic symmetry though. For example some things need to turn all the way around twice to get back to the same image.

Try solving X^2 = -I for 2x2 real matrices.
Protip: there are solutions.
No imaginary numbers needed.
The solutions are the rotations by plus or minus 90 degrees.
a+bi is represented by the matrix [a, b; -b, a] (or [a, -b; b, a] according to your convention).
Addition and multiplication behave the way they should.
If you take an arrow and rotate it by 90 degrees twice, it will be pointing in the opposite direction.
This shit isn't really that complicated.
>based on how we define multiplication and squaring and shit like that
Your mind is just broken and cannot abstract away from the analogical crutches you lean upon. If you are first learning how to walk, the crutches might be useful. Once you can walk without them, they are just in the way.

Lewis Carroll go home

...

Fucking nice

They're imaginary, only autistic people use them