>imaginary numbers
Imaginary numbers
Gabriel James
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Caleb Allen
>negative numbers
Thank god for imaginary numbers.
James Bailey
>you will never define a unit matching the usefulness of i
Angel Jackson
>Frogposting
Jeremiah Cox
They aren't real so, let's call them "imaginary"? I think that was the line of thinking.
Adam Rodriguez
>being a filthy normie
Electrical engineers are eternally indebted to the man who invented i.
Zachary Watson
>Frogposting
Matthew Gonzalez
I dropped out of highschool, and now after a couple NEET years, I've been really interested in math again. Studying totally on my own is kind of challenging though, and I'm having some trouble with this particular subject.
But anyway, what are these sons of bitches useful for? I get that i^2=(-1), but where can I actually use that?
If some nice user could give me a quick rundown, I'd be grateful.
Anthony Ross
The first really big deal is it gives every polynomial equation P(z)=0 at least one solution
From there, things you solve using polynomials, like some differential equations, can be solved
Then you get into stuff like e^(i x)=cos(x)+i sin(x), which is relevant for solving even more DEs.
Then there's the whole field of complex analysis to get into, with applications going into shit like conformal mapping.
Elijah Robinson
Lets say you want to solve an equation like [math] x^2 + 1 = 0 [/math], the fundamental theorem of algebra guarantees us a solution, but what is it, clearly it can't be 1 since 1^2+1 =2, likewise it can't be -1 since (-1)^2 =1. So we just define the solution to be [math] i [/math].
There's more complex examples, but that's the genesis of the idea.