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yooo you're in luck.. I'm taking a course in complex variables.

What are imaginary numbers?
Not real......

basically an imaginary number's an ordered pair

its when you try to take the square root of a negative number

There is only one imaginary number, i, defined by i^2 = -1

not really... a+bi are all imaginary.. a is the real part, b is the imaginary part.

b is real

you guys are confusing this student, lol

Stir,stir......

i is appended to the real number system by fiat......

lol

which is defined by:
(a,b)(c,d) = (ac-bd, ad+bc)

this conversation is really good for this student, keep it up guys

i meant i is an ordered pair, (0,1)

Then you make up an imaginary plane to go with this imagijnary number.....

Then the student says "Does it work in 3D?"

lol,

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.

I was like WOOOOOOOOOOOOOOWW

The real wow comes from http://en.wikipedia.org/wiki/Euler%27s_identity .

yea that too.. i need to read its proof

the sqrt of -1 came from messing about with negative logs....

it seems that you don't know badrefs lol

never heard of that one estudier..

That's because I'm on very intermittently. I can't get to know everyone around here.

Yeah, logarithms provided the construction of imaginaries. Let me pull one up.

my professor lied to me.... :/

Because in physics we were more concerned with the "existence" of things.

That explains it. I can't find the reference right now, sorry. :<

Let me see if I can dig it up.....

"They" being Bernoulli and Euler

Anyway, the point is ln(-1) = pi*i