How does this compute

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Offline syhprum

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How does this compute
« on: 18/12/2011 18:51:31 »
e^i pi = -1 how does this come about
syhprum

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Offline imatfaal

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Re: How does this compute
« Reply #1 on: 19/12/2011 10:38:20 »
In simplistic terms because if you plug [tex] \pi[/tex] into Euler's Formula the answer is -1

Euler's formula states that

[tex] e^{ix}=cos(x) + isin(x)[/tex]

as [tex]sin(\pi)= 0[/tex] and [tex]cos(\pi) = -1 [/tex] then [tex]e^{i\pi} = -1 + 0[/tex]

It can be demonstrated by using infinite series representations of both sides and showing they are equal. 

The actual "how it comes about" for Euler's formula is difficult - but you could think of the two sides of [tex] e^{ix}=cos(x) + isin(x)[/tex]  in terms of unit circles.  [tex] cos(x) + sin(x)[/tex] traces a unit circle of circumference [tex] 2\pi[/tex] radians on the real number plane and conversely [tex]e^{ix}[/tex] could be said to trace a unit circle on the complex number plane as x varies through real numbers
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Offline syhprum

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Re: How does this compute
« Reply #2 on: 19/12/2011 20:36:07 »
I found it rather puzzling at first as to why the answer did not contain any imaginary parts but when I found out sin/cos functions were iinvolved that can take any value between +1 to -1 including zero all became clear

P.s wheres the spell checker ?
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Offline Don_1

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Re: How does this compute
« Reply #3 on: 22/12/2011 08:00:37 »
[tex] \pi[/tex] into Euler's Formula the answer is -1

Euler's formula states that

[tex] e^{ix}=cos(x) + isin(x)[/tex]

as [tex]sin(\pi)= 0[/tex] and [tex]cos(\pi) = -1 [/tex] then [tex]e^{i\pi} = -1 + 0[/tex]
Euler's formula
[tex] e^{ix}=cos(x) + isin(x)[/tex] 
[tex] cos(x) + sin(x)[/tex]
[tex] 2\pi[/tex]
conversely [tex]e^{ix}[/tex]




P.s wheres the spell checker ?


Spell checker!!! Never mind the spell checker, where's the algebra checker???
If brains were made of dynamite, I wouldn't have enough to blow my nose.

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Offline imatfaal

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Re: How does this compute
« Reply #4 on: 22/12/2011 10:09:44 »
Spell checker!!! Never mind the spell checker, where's the algebra checker???

I was very pleased with my pretty new latex euler

on your marks, get set,.... pun!
There’s no sense in being precise when you don’t even know what you’re talking about.  John Von Neumann

At the surface, we may appear as intellects, helpful people, friendly staff or protectors of the interwebs. Deep down inside, we're all trolls. CaptainPanic @ sf.n

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Offline syhprum

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Re: How does this compute
« Reply #5 on: 23/12/2011 19:47:33 »
I have "Wolfram Mathmatica" but little skill in using it and would like to run thru the proof of Eulers  Formula which I find very elegent.
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Offline Geezer

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Re: How does this compute
« Reply #6 on: 23/12/2011 20:12:55 »
I was very pleased with my pretty new latex euler


Did you get a slide euler?
There ain'ta no sanity clause, and there ain'ta no centrifugal force æther.

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Offline syhprum

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Re: How does this compute
« Reply #7 on: 23/12/2011 20:34:56 »
When my son started technical high school about five years after pocket calculators got common I had to buy him a slide rule !.
I wonder how many companies still use them.
syhprum