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badreferences
 3 years 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
badreferences
 3 years 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

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bahrom7893
 3 years ago
Best ResponseYou've already chosen the best response.0yooo you're in luck.. I'm taking a course in complex variables.

bahrom7893
 3 years ago
Best ResponseYou've already chosen the best response.0uhmm I don't have a scanner at home, but msg me your email, I'll scan my notes tomorrow and email them to you.

estudier
 3 years ago
Best ResponseYou've already chosen the best response.2What are imaginary numbers? Not real......

bahrom7893
 3 years ago
Best ResponseYou've already chosen the best response.0basically an imaginary number's an ordered pair

heedcom
 3 years ago
Best ResponseYou've already chosen the best response.0its when you try to take the square root of a negative number

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

bahrom7893
 3 years ago
Best ResponseYou've already chosen the best response.0not really... a+bi are all imaginary.. a is the real part, b is the imaginary part.

heedcom
 3 years ago
Best ResponseYou've already chosen the best response.0you guys are confusing this student, lol

bahrom7893
 3 years ago
Best ResponseYou've already chosen the best response.0if 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.

estudier
 3 years ago
Best ResponseYou've already chosen the best response.2i is appended to the real number system by fiat......

bahrom7893
 3 years ago
Best ResponseYou've already chosen the best response.0which is defined by: (a,b)(c,d) = (acbd, ad+bc)

heedcom
 3 years ago
Best ResponseYou've already chosen the best response.0this conversation is really good for this student, keep it up guys

bahrom7893
 3 years ago
Best ResponseYou've already chosen the best response.0i meant i is an ordered pair, (0,1)

estudier
 3 years ago
Best ResponseYou've already chosen the best response.2Then you make up an imaginary plane to go with this imagijnary number.....

badreferences
 3 years ago
Best ResponseYou've already chosen the best response.0The 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.

estudier
 3 years ago
Best ResponseYou've already chosen the best response.2Then the student says "Does it work in 3D?"

bahrom7893
 3 years ago
Best ResponseYou've already chosen the best response.0i^2 = i*i = (0,1)(0,1) = (0*01*1,0*1+1*0)=(1,0)... that's where i^2 = 1 came from.

bahrom7893
 3 years ago
Best ResponseYou've already chosen the best response.0I was like WOOOOOOOOOOOOOOWW

badreferences
 3 years ago
Best ResponseYou've already chosen the best response.0The real wow comes from http://en.wikipedia.org/wiki/Euler%27s_identity .

bahrom7893
 3 years ago
Best ResponseYou've already chosen the best response.0yea that too.. i need to read its proof

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

estudier
 3 years ago
Best ResponseYou've already chosen the best response.2the sqrt of 1 came from messing about with negative logs....

bahrom7893
 3 years ago
Best ResponseYou've already chosen the best response.0it seems that you don't know badrefs lol

bahrom7893
 3 years ago
Best ResponseYou've already chosen the best response.0never heard of that one estudier..

badreferences
 3 years ago
Best ResponseYou've already chosen the best response.0That's because I'm on very intermittently. I can't get to know everyone around here.

badreferences
 3 years ago
Best ResponseYou've already chosen the best response.0Yeah, logarithms provided the construction of imaginaries. Let me pull one up.

bahrom7893
 3 years ago
Best ResponseYou've already chosen the best response.0my professor lied to me.... :/

badreferences
 3 years ago
Best ResponseYou've already chosen the best response.0Not necessarily. I learned something else in math. In physics we constructed Platonic imaginaries through logs.

badreferences
 3 years ago
Best ResponseYou've already chosen the best response.0Because in physics we were more concerned with the "existence" of things.

estudier
 3 years ago
Best 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:)

badreferences
 3 years ago
Best ResponseYou've already chosen the best response.0That explains it. I can't find the reference right now, sorry. :<

estudier
 3 years ago
Best ResponseYou've already chosen the best response.2Let me see if I can dig it up.....

badreferences
 3 years ago
Best ResponseYou've already chosen the best response.0Save us @estudier !

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

estudier
 3 years ago
Best 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)..."

estudier
 3 years ago
Best ResponseYou've already chosen the best response.2"They" being Bernoulli and Euler

estudier
 3 years ago
Best ResponseYou've already chosen the best response.2Anyway, the point is ln(1) = pi*i

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

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

estudier
 3 years ago
Best ResponseYou've already chosen the best response.2Take 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
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