>>16945828
Skill issue. They arise quite naturally when you try to extend the rational or real numbers. All it takes is:
1. there is a set [math]\mathbb{S}\supset\mathbb{R}[/math] that forms a number field, this implies there is at least one new number in it, meaning [math]\exists x\in\mathbb{S}:x\not\in\mathbb{R}[/math]
2. knowing only x and the reals, you can construct every element of [math]\mathbb{S}[/math] through arithmetic (addition, multiplication, division) in a limited number of steps.

Turns out, that limited number can always be simplified to 2 and the only solution is the complex numbers.

>>16945860
replacing x with any finite number of new numbers changes nothing, and all but one are gonna end up redundant.
Complex numbers are pretty goddamn unique in that regard.

>>16945828
Sqrt(-1) = i
There. You now understand imaginary numbers.

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you don't need to understand.

>>16945828
they do make sense, it's just the name that filters people

>>16945828
Perhaps you lack the proper degree of imagination necessary to make sense of them in your own head.

>>16945828
Skill issue.
If you can't make sense of the imaginary unit there is no hope you can fathom the hyperbolic unit.
[math]j^2=+1,\; j\notin\mathbb{R}[/math]

>>16950129
gay because no multiplicative inverse

They're literally just 2D numbers, mathfag midwits are too pretentious to admit it's that simple so they try to obfuscate the truth to look smart.

>>16945828
6 million fake numbers. not even real

>>16957063
>2D numbers
go jerk off to anime, fag

>>16945828
I'm pretty sure they're just an esoteric way of representing a point on a 2-axis graph. Someone correct me if I'm wrong, this isn't my field.

>>16957157
the beautiful thing is that they represent both the points AND the operators to rotate/move points

>>16957157
Negative number : Rotation 180° (or Pi) clockwise or counterclockwise.
Multiply by i : Rotation 90° (or Pi/2) counter clockwise.

>>16957063
>>16957157
The complex plane is a useful model but the reality is much simpler still:
See >>16946219
Literally everything else is downstream of that.

>>16945828
>ask a philosophical question
>every answer in this thread is technical, not philosophical

>>16945828
Because you refuse to practice your fundamentals.

>>16957532
Philosophically speaking, OP's question is is based on a false premise. It's like asking "why can't birds fly?"
The correct response it to explain "yes they can" and elaborate.

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>>16945828
"i" simplify the use of matrices, same with the negative symbol "-".
You cant easily teach the average highschooler how to use matrices, but you can teach them "if you square it, just add a minus symbol in front, dont ask".
If some guys go to College, they will learn the inner signification of "i" and its powerful usefulness, picrel is a well known example.

Also this if you like vectors instead of matrices :
>>16957254

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>>16945828
>>16957532
I have a philosophical answer.
so the root of it is... it's a piece of magic from the inner planes. The ultimate truths often look contradictory/paradoxical when viewed through the outer mind.
Imaginary/complex numbers are so elegant and useful that they cant be fake/incorrect.
But -- = + and ++ = + in the tangible plane e.g. removing from a cost (sale) is a gain, or adding to a gain is a gain (e.g. raise + salary).
So overtly the -- -> - or ++ -> - of i is incorrect. Therefore it is not an outer plane thing.
The complex numbers are essentially more fluid, mutable, mixable... and paradoxical - therefore they refer to phenomena on a deeper level of existence (inner, subjective, higher order, platonic).
The reals are ... more tangible and mundane.
The answer is to accept the paradox(es) and hold space for them without doubt and without trying to force "only one side is correct".
>O the depth of the riches both of the wisdom and knowledge of God! How unsearchable are His judgments, and His ways past finding out!
>picrel: Leibniz knew.