>imaginary numbers

>>8762959
>negative numbers

Thank god for imaginary numbers.

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>>8762959
>you will never define a unit matching the usefulness of i

>>8762959
>>8762981
>Frogposting

>>8762959
They aren't real so, let's call them "imaginary"? I think that was the line of thinking.

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>>8762982
>being a filthy normie
>>8762984
>>8762981
Electrical engineers are eternally indebted to the man who invented i.

>>8762989
>Frogposting

>>8762959
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 anon could give me a quick rundown, I'd be grateful.

>>8762992
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.

>>8762992
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.

>>8762959

>imaginary shitposting

>>8762992
To give a specific use that is relevant to every day life, imaginary numbers are extremely useful when analyzing alternating current circuits, since they let you account for phase shift inside algebraic equations - the i works out to the exact same thing as shifting a vector 90 degrees with the whole e to the i pi thing. Makes life a lot easier.

>>8762992

The most obvious answer is that it gives us a method to solve differential equations, by using Euler's Identity.

Differential equations model how things change using mathematics. You know how there are graphs that show how things change over time and then we use those graphs to predict things that will happen in the future? That's differential equations, and many of them use imaginary numbers.

Don't get tripped up by the "imaginary" part. They're not imaginary. "Complex numbers" are a much more useful jargon.

>>8762959
>""""""""""imaginary"""""""""" numbers
the worst nomenclature in all of STEM desu

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>>8762959
>real brainlets

https://www.youtube.com/watch?v=F_0yfvm0UoU

IT ALL MAKES SENSE NOW

Haha salty mathcucks who spend their time working on numbers that aren't even real

>>8762959
Brainlet OP never heard of quaternions

>>8763003
>derp the soultion doesnt exist but muh flawed fundemental theory says it has to have at least one
>derp lets invent the solution

>>8763147
> what are algebraic field extensions

>>8763153
>using fancy words to mask the obvious hack

>>8763147
>flawed fundemental theory

One, it's a theorem. Two that's not how theorems work.

>>8763003
>genesis of the idea
Actually it came from cubic polynomials in Italy in the 16th century.

https://youtu.be/_qvp9a1x2UM?t=2m20s

>same two digits in the post number

>>8763147
I like fractals.

Used to have so much trouble solving equations like
let z = a+j*b
Find sqrtz in terms of c+j*d.
Now I'm thinking how stupid i must have been.

>real numbers
>as imaginary as imaginary numbers

>>8762992
>imaginary numbers exist in several dimensions
>capable of imparting rotations
>have complex analysis research symposiums around the world
>believed to be related to quaterions and possibly octonions
>at this very moment in contact with complex algebras

>>8762992
Heres a quick rundown:
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>in contact with aliens
>rumoured to possess psychic abilities
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>own castles and banks all over the world
>direct descendants of the ancient royal blood line
>will bankroll the first cities on Mars (Bogdangrad will be be the first city)
>own basically every DNA editing research facility on Earth
>first designer babies will be Bogdanoff Babies
>both brothers said to have 400+ IQ
>ancient Indian scriptures tell of two angels who will descend upon the Earth and will bring an era of enlightenment and unprecedented technological progress with them
>These are the Bogdanoff twins
>They own Nanobot R&D labs around the world
>You likely have Bogdabots inside you right now
>The Bogdanoffs are in regular communication with the Archangels Michael and Gabriel, forwarding the word of God to the Orthodox Church
>They learned fluent French in under a week
>Nation states entrust their gold reserves with the twins. There's no gold in Ft. Knox, only Ft. Bogdanoff
>The twins are 67 years old, from the space-time reference point of the base human.
>In reality, they are timeless beings existing in all points of time and space from the big bang to the end of the universe
>The Bogdanoffs will guide humanity into a new age of wisdom, peace and love