So
What are the complex numbers? why were they created and how did they came with the ideia of add a real number with ''something'' to get to a point? what and where is this point?
Complex Numbers
James Peterson
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Kevin Bell
Defining the square root of a negative number yields i. From there you can form the complex shit.
Dominic Perez
Real numbers sit on a one-dimensional real line.
Extend this line with one extra dimension and you get a two-dimensional complex space. You still have all the real numbers but now you can move along the complex dimension as well.
Kevin Richardson
Let's say you want to find the roots of the polynomial x^2 + 1.
What are they?
That kind of question led to the invention of the complex numbers as a way to give every polynomial at least one root.
It happened, IIRC, in the 1500s with people like Cardano and root finding competitions that people used to show off.
Joseph Kelly
this shit is making more sense now, although math will always be for the crazy ones
Isaac Smith
>What are the complex numbers?
Take the cartesian product of the set of real numbers with itself and then take the ordered pairs this results in and while no one is looking paint a cute little 'i' next to the second component.
That is your geometric definition of the complex plane.
While every mathematician is still not looking you have to figure out what will this little i you painted be for.
You could decide for anything but you just randomly decide that you want to have your new set be closed under the root operation so you make your i equal a root that is not real. You could say that i is the root of -2, or -500000000 and it would all be the same, but for simplicity you choose i to be the root of -1
Now you can literally perform any standard operation on your set and you can also solve every polynomial equation.
That said, there are probably a billion ways to make a system in which we can solve all polynomials but this is probably the most intuitive.
Owen Powell
The idea was to use them for temporary calculations and then reduce to get a real solutions.
They weren't used for quadratic equations originally but 4th degree equations
Daniel Hughes
My math professor explained it once he introduced the complex numbers. Look up the history.
Cardano, Gauß, Cauchy and even Kant will help you out on that.
Elijah Phillips
I know this will take your motivation to learn math, but I have to tell you what I think is the truth, since you asked. I do recommend that you learn math, that you call yourself a mathnoob and all that.
Complex Numbers, and more specifically, negative roots are Bad math. Bad math is accepted on a rush for rhetorical reasons, like the artificial complexity involved in it. Why this happens? The complexity is what attracts smart people around this part of math and results in useful things coming out of it. I say this believing that you already accept that smart people are attracted to complexity.
I wish I am wrong though, that my knowledge about this is plain superficial and emotional, because I rather live in a world where people don't fuck mathematics up.
But as far as I know, modern mathematics is a mess, taught by people without interest in proofs and good definitions. It ends up being a brainwashing that makes dependent slaves instead of conscious workers, your general problem solving ability is diminished by it afterwards instead of increased. I can go on and on about this, consider the terms that you use in math: reals, complex, integrals, calculus... etc these are terms designed to castrate you mentally.
Benjamin Richardson
Algebraic closure of the reals.