Some math stuff...

[HINDYhat]

So I've been recently messing around in math class, and now I've found something that I can't solve... and neither can my math teacher xD.

Let's start with this formula:
e^(pi*i) = -1
Which has been proven because:
e^(x*i) = cos x + isin x
I think that's "Euler's formula" or something along those lines.

Now, if I square both sides...
(e^(pi*i))^2 = (-1)^2
e^(2*pi*i) = 1

And now I put it in logarithmic form:
ln e^(2*pi*i) = ln 1
2*pi*i = ln 1
2*pi*i = 0

Which is completely untrue... so I must be messing up somewhere...

Where have I screwed up???

 

[Elenai]

You screwed up when you took math class.

On topic:

Did you use order of operations?

I am more of a history major than a mathmatics major...so I may not know what I am talking about.

 

[donut3.5]

Haha when I put in
ln(e^(2*pi*i)) into my calculator, it did come up with 0..
Then when I did 2*pi*i it came up with ~6.28i..
--donut3.5--

 

[Elenai]

It is most likley the way the numbers work in accordance to the formula.

As Pi, is (3.14.....blah blah....blah...blah...another decimal......forevermore continuing.) It may give an answer different from one were it is the square of "e".

Isnt a square root a fraction of some kind. Using the square root number (like the cube root [3] of a number is 3/# or something of that sort)

 

[HINDYhat]

As far as I know, order of operations in this case is kinda useless, since logs have so many ways to be solved... they should all come up with the same answer... except this one.

Well this one can be proven with:
ln e^(2*pi*i) = ln (cos 2*pi + isin 2*pi) = ln 1
THAT part works... but solving using:
ln e^x = x
doesn't work at all...

 

[Elenai]

Order of operations is never useless HINDYhat. It is one of the basic corner stones of mathmatics.

Even at high levels of mathmatics, Order of Operations, is precedent.

3+3*2

using OOO it comes out correct as 9 (I wont insult your intelligence, I'm sure you know that)

Without it...it is 12...A +3 change.

And so you must follow order of ops. Perhaps that is what you are doing wrong?

Then again...I am not a math expert.

 

[HINDYhat]

How would that come out as 36, even without following order of operations?

Using order of operations: (3*2) + 3 = 6 + 3 = 9
Without order of operations : (3+3) * 2 = 6 * 2 = 12
Still the wrong answer, but still not 36

I really don't know... my teacher would've had pointed that out, no? Anyway, just try with any other logarithm problem... they're generally solvable in many ways.

 

[Elenai]

WOOPS! Sorry...its twelve....my mistake.

I was thinking 6*6

BLONDE MOMENT!!!!...even though I am not blonde.

:Edited post:

 

[Mechanical Man]

Note that when squaring equation you get also non correct solutions.

 

[Modo]

Is this University Level maths, or just high school. I will ask my friends about it when I can. Most of them were aces at maths in high school. I think some of them take it at uni as well.

 

[HINDYhat]

No idea, probably Uni. I'm not at that level yet... I teach myself

 

[-JonNny]

The first line can NOT be true or proven i think because "e^x" is always positive ! no matter what x is
f(x ) = e^x
x-> + infinity / f(x ) -> + infinity

x-> - infiity / f(x ) -> 0 (Asymptote!!)


and if you assume "2*pi*i = 0" it would be e^0 which is of course "1"
but "2*pi*i" does not look like zero to me

maybe im wrong... however

Edit :
Hmm... i also found "e^(pi*i) = -1" ... now im confused :S


"i" is the imaginary number which can just exist imaginary and not in reality.
for example x²+1 = 0 or Sqrt(-x) .. solution is always +- i or sth
so i² can be -1

i element of C

:> looks interesting , i hope were going to do this in school soon

 

[PurplePoot]

To -JonNny

Most peoples' brains would implode if you did that in school (and this includes your teachers by the way), this is probably either university-level or beyond. (My g12 math teacher doesn't know this stuff... so I don't bother trying to ask him when I have to solve crazy stuff like this )

By the way, I think the correct "element of" thingee (let's pretend that element sign is > for purposes of ASCII) N > W > I > Q > R > C

(Assuming N = Natural W = Whole I = Integer Q = Rational R = Real C = Complex)

As for the actual thread topic:

You're not doing anything wrong, except not realizing 2*pi*i does equal 0 in this case

You're forgetting that in radians 2pi = 0, so that formula is correct when working with angles (as there), but not when working with basic math (well, it couldn't be anyways), because Cos/Sin do a modulus calculation to avoid getting ridiculous results as lim x->∞

And yes, e^ix = cos x + i sin x is Euler's Formula, just as e^ipi + 1 = 0 is Euler's Identity.

Elenai, Order of Operations has no place in an equation that's actually just a mess of functions... it definitely doesn't matter here.

Note that when squaring equation you get also non correct solutions.

Elaborate.

 

[HINDYhat]

Oh, I guess I forgot the most idiotic thing ever. Some math dude just told me.

ln e^x = x
ONLY if x ∈ R!!

... lame error -.-. My math teacher should be ashamed of herself

 

[PurplePoot]

That too =o

Same idea that Sqrt(nn) = Sqrt(n)Sqrt(n) only if n>0