anonymous
  • anonymous
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/what-are-imaginary-numbers
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
bahrom7893
  • bahrom7893
yooo you're in luck.. I'm taking a course in complex variables.
bahrom7893
  • bahrom7893
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.
anonymous
  • anonymous
What are imaginary numbers? Not real......

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bahrom7893
  • bahrom7893
basically an imaginary number's an ordered pair
anonymous
  • anonymous
its when you try to take the square root of a negative number
anonymous
  • anonymous
There is only one imaginary number, i, defined by i^2 = -1
bahrom7893
  • bahrom7893
not really... a+bi are all imaginary.. a is the real part, b is the imaginary part.
anonymous
  • anonymous
b is real
anonymous
  • anonymous
you guys are confusing this student, lol
anonymous
  • anonymous
Stir,stir......
bahrom7893
  • bahrom7893
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.
anonymous
  • anonymous
i is appended to the real number system by fiat......
anonymous
  • anonymous
lol
bahrom7893
  • bahrom7893
which is defined by: (a,b)(c,d) = (ac-bd, ad+bc)
anonymous
  • anonymous
this conversation is really good for this student, keep it up guys
bahrom7893
  • bahrom7893
i meant i is an ordered pair, (0,1)
anonymous
  • anonymous
Then you make up an imaginary plane to go with this imagijnary number.....
anonymous
  • anonymous
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.
anonymous
  • anonymous
Then the student says "Does it work in 3D?"
anonymous
  • anonymous
lol,
bahrom7893
  • bahrom7893
i^2 = i*i = (0,1)(0,1) = (0*0-1*1,0*1+1*0)=(-1,0)... that's where i^2 = -1 came from.
bahrom7893
  • bahrom7893
I was like WOOOOOOOOOOOOOOWW
anonymous
  • anonymous
The real wow comes from http://en.wikipedia.org/wiki/Euler%27s_identity .
bahrom7893
  • bahrom7893
yea that too.. i need to read its proof
anonymous
  • anonymous
it seems the questions stater already knew much info but wanted to see how we explain complex numbers, lol
anonymous
  • anonymous
the sqrt of -1 came from messing about with negative logs....
bahrom7893
  • bahrom7893
it seems that you don't know badrefs lol
bahrom7893
  • bahrom7893
never heard of that one estudier..
anonymous
  • anonymous
That's because I'm on very intermittently. I can't get to know everyone around here.
anonymous
  • anonymous
Yeah, logarithms provided the construction of imaginaries. Let me pull one up.
bahrom7893
  • bahrom7893
my professor lied to me.... :/
anonymous
  • anonymous
Not necessarily. I learned something else in math. In physics we constructed Platonic imaginaries through logs.
anonymous
  • anonymous
Because in physics we were more concerned with the "existence" of things.
anonymous
  • anonymous
@bahrom7893 - that's cos complex analysis is for pure mathematicians (they have to justify their existence, y'see:-)
anonymous
  • anonymous
That explains it. I can't find the reference right now, sorry. :<
anonymous
  • anonymous
Let me see if I can dig it up.....
anonymous
  • anonymous
Save us @estudier !
anonymous
  • anonymous
This might be it http://www.maa.org/editorial/euler/How%20Euler%20Did%20It%2046%20e%20pi%20and%20i.pdf
anonymous
  • anonymous
"...They were perplexed because they had equally convincing (and flawed) arguments to "prove" that ln(-x) = ln(x)..."
anonymous
  • anonymous
"They" being Bernoulli and Euler
anonymous
  • anonymous
Anyway, the point is ln(-1) = pi*i
anonymous
  • anonymous
I'll try to post something as to how you can get a quantity that evaluates to -1 without all the hoopla.....
anonymous
  • anonymous
A really amusing question from Math Underflow http://math.stackexchange.com/questions/202172/why-is-i-0-498015668-0-154949828i What does \(i!\) evaluate to?
anonymous
  • anonymous
Take a pair of vectors uv with the normal rules for multiplication etc and so write uv = 1/2(uv+vu) + 1/2(uv-vu) 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|^2|v|^2sin^2 theta So whatever u wedge v is, it's square is a negative scalar

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