Solve

1/x = -x.  solve for x.

i, -i

/thread

x^2+1 > 0 for all x in R

>>1
Impossible since it involves -, therefore i, -i.

>>3
what?

>>2
i is a cop out. Real mathematicians will tell you this equation is unsolvable.

>>5
Complex analysis.

>>5
GBT middle school

-1, lol!

>>8
Fail, hard
>>7
lurk moar

-1*-1=1

>>10
yes, so?

>>9

((1)/(-1)) = ((-1)/(1)) = -1, lol!

oh, wait.  How did I not see the - in -x this whole time?  I must need reading glasses.  +-i it is, then.

>>13
, lol!

>>11
x=-1
-x=1

>>13
Give an exact figure for "i".

>>16
i is such that 0i = 1.

>>16
i*i = -1
don't be a faggot

>>16
here:
i

What could iⁱ possibly signify?

>>20
= (e^i*pi/2)ⁱ = e^-pi/2

>>18
ok, calculate (-1)^0.5

>>21
I know what it might equal, but I'm more interested in what iⁱ can SIGNIFY.  What does it signify to take an imaginary number (essentially, a negative dimension) and then take it to an imaginary power?

>>23


The powers of real and imaginary numbers are generally defined in terms of the exponential function.

things like 2^3 have obvious meanings, but a^b for arbitrary a and b in the reals the meanings not so clear.

So using the exponential function which is quite easy to define in terms of real numbers, and it's inverse the logarithm we say that.

a^b = exp(b*log(a))

which has a definite expression in terms of real power series that we know converge (Given certain restrictions on a)


This can then be extended quite easily for complex a and b, given that we first extend our definitions of the complex exponential and logarithmic functions.

Make sense?

>>23

it works, it's consistent, it's beautiful.  gb2 high school

>>24
Wow.  Just wow.  lrn2mathematics

>>23
What do you mean by "signify"?  2³ = 2*2*2?

2^sqrt(3) = pwnt... the best you can do is define it as limit{2^x, x -> sqrt(3)}; have fun taking the 1.7 billionth power of the billionth root of 2.

In complex analysis (at least this crappy book by Brown & Churchill),
log(i) = {i*pi/2 + 2*pi*i*n | n is integer}
Log(i) = i*pi/2 (principle value)

If you notice in >>24's definition, it allows iⁱ to be an infinite set, namely {e^{-pi(2n + (1/2))} | n is integer}.

>>25
shut up you queen, go to a board for people who already know everything

calculate (-1)^0.5 or you lose and are an idiot, sorry

>>29
i, faggot
btw i'm imagining plowing you in the ass right now

>>26


lrn 2 mathematics?
you trolling nigger? It makes perfect sense.

I'm sure there are other, equivalent ways of defining that shit, but this ways the way I was taught and it seems to follow quite simply from basic concepts.

>>27
For me, "signify" means "forms a more comprehensive symbol".  It's an appeal to make things less abstract.  Just pushing the symbols around is not enough; in order to become functional in math, I've found it necessary to find what things signify.

I've already signified i as a "negative dimension".  Giving that definition to it other than "it's an imaginary number" simply has more significance in my mind.

Hence, when I take this negative dimension and take it to the power of a negative dimension, then what "more comprehensible" (even, "more commonly experienced") thing does that signify?

Taking any real number to the power of another rational number isn't a particularly good model, since now I'm dealing with the imaginary numbers.  They could have other properties.

Hey, I was just curious.  Hence, I wondered what other 4channers thought about it.

>>30
i is just an algebraic symbol like x and y in graphs. It's not a number. Give me the number.

>>33
x, y are generally variables (ie not always the same value)
i is always the same constant (ie always the same value) (up to isomorphism with -i)

i is an imaginary number

If you're thinking about decimal expansions, then phail, since that can only represent finite real numbers.

>>32
I've generally visualized things according to their algebraic properties (ie pushing symbols around), so I can't help you with that.

Even 4 dimensions is incredibly difficult to visualize; I'm not sure how you manage to visualize negative dimensions.  Do describe.

My example was not intended to demonstrate the properties of exponentiation, but rather to demonstrate that even in a relatively simple case, intuition falls apart.  If you can find a less abstract way to visualize the sqrt(3)th power of a positive real number, I'd love to hear it.

>>33
no, you cunt
i is a complex number
this is starting to piss me off

if you're serious, i'm going to hunt you down and ram a math book up your ass.

if you're trolling, i'm going to hunt you down and rape you

so, which is it?

>>32

I've already signified i as a "negative dimension".

what?

Why not just deal with abstract concepts, it's not that hard.

>>34
I discovered that i represented a negative dimensioning.  Construct a Cartesian plane, but use i for the axes.  You'll notice soon that AREAS on that plane are real numbers (i.e. the area between 0 and y +1i and x +1i is -1).

Since on the i plane (constructed of dimensionality 1 numbers), real numbers are areas (dimensionality 2), then our real numbers just sitting alone (dimensionality 0) may sit in a dimensionality number just 1 above what the i numbers do.  Hence, a dimensionality of 0-1, hence -1, hence a "negative dimension".

Thinking about this some more, I concluded that a good way to visualize this is with a black hole or other puncture through our universal fabric.  Negative dimensionality seems to represent a universe beneath or beyond ours ... and in that universe, you can use i in the same algebraic fashion as our 0-dimension numbers are.

However, I find myself on unstable ground with all this amateur crap, and when I posted about iⁱ, I was unable to come up with a visualization.  Hence, I feel I can't signify it.

>>33
Define number, whore.

>>34
If it is a constant then you should be able to give me a figure. Even though we do not know the exact figure for Pi we know it is between 3.14159265358 and 3.14159265357. You must do the same for i.

>>35
If complex numbers are not numbers. "i" is an algebraic symbol in an equation, not a number.

>>34
>>35
Calculate i.