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What are imaginary numbers? Well, wonder no more. This is the most solid explanation I could find online, and it's really good.
http://math.stackexchange.com/questions/199676/whatareimaginarynumbers
 one year ago
 one year ago
What are imaginary numbers? Well, wonder no more. This is the most solid explanation I could find online, and it's really good. http://math.stackexchange.com/questions/199676/whatareimaginarynumbers
 one year ago
 one year ago

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bahrom7893Best ResponseYou've already chosen the best response.0
yooo you're in luck.. I'm taking a course in complex variables.
 one year ago

bahrom7893Best ResponseYou've already chosen the best response.0
uhmm I don't have a scanner at home, but msg me your email, I'll scan my notes tomorrow and email them to you.
 one year ago

estudierBest ResponseYou've already chosen the best response.2
What are imaginary numbers? Not real......
 one year ago

bahrom7893Best ResponseYou've already chosen the best response.0
basically an imaginary number's an ordered pair
 one year ago

heedcomBest ResponseYou've already chosen the best response.0
its when you try to take the square root of a negative number
 one year ago

estudierBest ResponseYou've already chosen the best response.2
There is only one imaginary number, i, defined by i^2 = 1
 one year ago

bahrom7893Best ResponseYou've already chosen the best response.0
not really... a+bi are all imaginary.. a is the real part, b is the imaginary part.
 one year ago

heedcomBest ResponseYou've already chosen the best response.0
you guys are confusing this student, lol
 one year ago

bahrom7893Best ResponseYou've already chosen the best response.0
if a=0, the number is called pure imaginary.. Idk otherwise my professor was lying to me. No we're not, everyone knows that i is imaginary.
 one year ago

estudierBest ResponseYou've already chosen the best response.2
i is appended to the real number system by fiat......
 one year ago

bahrom7893Best ResponseYou've already chosen the best response.0
which is defined by: (a,b)(c,d) = (acbd, ad+bc)
 one year ago

heedcomBest ResponseYou've already chosen the best response.0
this conversation is really good for this student, keep it up guys
 one year ago

bahrom7893Best ResponseYou've already chosen the best response.0
i meant i is an ordered pair, (0,1)
 one year ago

estudierBest ResponseYou've already chosen the best response.2
Then you make up an imaginary plane to go with this imagijnary number.....
 one year ago

badreferencesBest ResponseYou've already chosen the best response.0
The link I provided in the OP is a solid construction of how we (us normal humans, and bahrom7893) conjectured the Platonic existence of imaginary numbers. For further reading, check out "Mathematics: Its Content, Methods and Meaning" by A.D. Aleksandrov, et al.
 one year ago

estudierBest ResponseYou've already chosen the best response.2
Then the student says "Does it work in 3D?"
 one year ago

bahrom7893Best ResponseYou've already chosen the best response.0
i^2 = i*i = (0,1)(0,1) = (0*01*1,0*1+1*0)=(1,0)... that's where i^2 = 1 came from.
 one year ago

bahrom7893Best ResponseYou've already chosen the best response.0
I was like WOOOOOOOOOOOOOOWW
 one year ago

badreferencesBest ResponseYou've already chosen the best response.0
The real wow comes from http://en.wikipedia.org/wiki/Euler%27s_identity .
 one year ago

bahrom7893Best ResponseYou've already chosen the best response.0
yea that too.. i need to read its proof
 one year ago

heedcomBest ResponseYou've already chosen the best response.0
it seems the questions stater already knew much info but wanted to see how we explain complex numbers, lol
 one year ago

estudierBest ResponseYou've already chosen the best response.2
the sqrt of 1 came from messing about with negative logs....
 one year ago

bahrom7893Best ResponseYou've already chosen the best response.0
it seems that you don't know badrefs lol
 one year ago

bahrom7893Best ResponseYou've already chosen the best response.0
never heard of that one estudier..
 one year ago

badreferencesBest ResponseYou've already chosen the best response.0
That's because I'm on very intermittently. I can't get to know everyone around here.
 one year ago

badreferencesBest ResponseYou've already chosen the best response.0
Yeah, logarithms provided the construction of imaginaries. Let me pull one up.
 one year ago

bahrom7893Best ResponseYou've already chosen the best response.0
my professor lied to me.... :/
 one year ago

badreferencesBest ResponseYou've already chosen the best response.0
Not necessarily. I learned something else in math. In physics we constructed Platonic imaginaries through logs.
 one year ago

badreferencesBest ResponseYou've already chosen the best response.0
Because in physics we were more concerned with the "existence" of things.
 one year ago

estudierBest ResponseYou've already chosen the best response.2
@bahrom7893  that's cos complex analysis is for pure mathematicians (they have to justify their existence, y'see:)
 one year ago

badreferencesBest ResponseYou've already chosen the best response.0
That explains it. I can't find the reference right now, sorry. :<
 one year ago

estudierBest ResponseYou've already chosen the best response.2
Let me see if I can dig it up.....
 one year ago

badreferencesBest ResponseYou've already chosen the best response.0
Save us @estudier !
 one year ago

estudierBest ResponseYou've already chosen the best response.2
This might be it http://www.maa.org/editorial/euler/How%20Euler%20Did%20It%2046%20e%20pi%20and%20i.pdf
 one year ago

estudierBest ResponseYou've already chosen the best response.2
"...They were perplexed because they had equally convincing (and flawed) arguments to "prove" that ln(x) = ln(x)..."
 one year ago

estudierBest ResponseYou've already chosen the best response.2
"They" being Bernoulli and Euler
 one year ago

estudierBest ResponseYou've already chosen the best response.2
Anyway, the point is ln(1) = pi*i
 one year ago

estudierBest ResponseYou've already chosen the best response.2
I'll try to post something as to how you can get a quantity that evaluates to 1 without all the hoopla.....
 one year ago

badreferencesBest ResponseYou've already chosen the best response.0
A really amusing question from Math Underflow http://math.stackexchange.com/questions/202172/whyisi04980156680154949828i What does \(i!\) evaluate to?
 one year ago

estudierBest ResponseYou've already chosen the best response.2
Take a pair of vectors uv with the normal rules for multiplication etc and so write uv = 1/2(uv+vu) + 1/2(uvvu) So that first term is basically u dot v and we'll call the second one u (wedge) v. uv = u.v + u wedge v vu = u.v  u wedge v Multiply these two uvvu = (u.v9^2 (u wedge v)^2 Since vv = v^2 > (u wedge v)^2 =u^2v^2sin^2 theta So whatever u wedge v is, it's square is a negative scalar
 one year ago
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