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![[Post New]](/templates/default/images/icon_minipost_new.gif) 2 Dec 2007 18:40:47 IST
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THEOREM: e=1
Proof:
let 2*e = f-------------->(1)
where f>0
rasing to the power 2*pi*i
(1)==>2(2*pi*i)e(2*pi*i) = f(2*pi*i)-------------->(2)
but,e(2*pi*i) = 1 (since from complex no.s , i.e. e(2*pi*i) =cos(2*pi)+i sin(2*pi) )
Therefore
(2)==>2(2*pi*i) = f(2*pi*i)
==>2=f (since power are equal bases can be equated)
Thus, from (1), we have....
e=1
rate me if u like the challenge
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2 Dec 2007 18:43:47 IST
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please do give me a detailed solution
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2 Dec 2007 20:00:31 IST
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rates assured to anyone who answers this question!!!!!!!
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2 Dec 2007 20:05:20 IST
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You've basically done it for a power that is irrational!!!
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Will nip in at times to solve problems :)
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2 Dec 2007 20:06:54 IST
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as in what? raising it to equal powers on both sides satisfies the equation ....be it any kind of power then.......
correct me if i am wrong!!!
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2 Dec 2007 20:07:22 IST
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Aby oye, Tumne likha hai (since powers are equal, base can be equated) This is no property. The real property is-when bases are equal, powers can be equated. According to what you have written it is also true that 12=22=32=.........=n2. Which is not true. Now I think you should give me a salute as you promised. 
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The quality of a person's life is in direct proportion to their commitment to excellence, regardless of their chosen field of endeavor.
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2 Dec 2007 20:08:07 IST
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What do you think about my explanation?
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The quality of a person's life is in direct proportion to their commitment to excellence, regardless of their chosen field of endeavor.
It is during our darkest moments that we must focus to see the light.
Check out my blog at:
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Posts:
Can marks really judge a student??
Some myths about Chemical Engineering.
(A must see for every student)
Back to goiit, this time with Baby Veerappan. :D |
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2 Dec 2007 20:11:52 IST
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Good catch Tarin.
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2 Dec 2007 20:14:29 IST
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hey tarin what ever you say is not wrong but it is also true that : an=bn then a=|b| isnt it
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2 Dec 2007 20:15:18 IST
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hey tarin what ever you say is not wrong but it is also true that : if an=bn then a=|b|............ isnt it this means if powers are equal then bases can be equated
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2 Dec 2007 20:18:23 IST
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Your point seems to be correct hemant. Wait let me think on it.
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The quality of a person's life is in direct proportion to their commitment to excellence, regardless of their chosen field of endeavor.
It is during our darkest moments that we must focus to see the light.
Check out my blog at:
http://tarinbansal.blogspot.com/
Posts:
Can marks really judge a student??
Some myths about Chemical Engineering.
(A must see for every student)
Back to goiit, this time with Baby Veerappan. :D |
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u reached 2 2 i = f 2i...fine write it as, e ln2^(2i) = e lnf^(2i)this becomes e 2ln2 i = e 2lnf i now write it as cos(2 ln2) + isin(2 ln2) = cos(2 lnf) + isin(2 lnf) so u can equate cos(2 ln2)=cos(2 lnf) n sin(2 ln2)=sin(2 lnf) this will have infinite solns but we must take only valid solns cos(2 ln2) = cos(2 lnf +/- 2n ) ln2=lnf - 1 ln2=ln(f/e) 2=f/e 2e=f
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<TABLE CELLSPACING="1" CELLPADDING="1" BORDER="0">
<TR><TD>
<DIV ALIGN="right">Animated Letters</DIV></TD></TR></TABLE>
I am only one,
But still I am one.
I cannot do everything,
But still I can do something;
And because I cannot do everything
I will not refuse to do the something that I can do.
- Edward Everett Hale
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2 Dec 2007 20:28:08 IST
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u can't directly equate bases when raised to complex powers
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<TABLE CELLSPACING="1" CELLPADDING="1" BORDER="0">
<TR><TD>
<DIV ALIGN="right">Animated Letters</DIV></TD></TR></TABLE>
I am only one,
But still I am one.
I cannot do everything,
But still I can do something;
And because I cannot do everything
I will not refuse to do the something that I can do.
- Edward Everett Hale
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2 Dec 2007 20:33:28 IST
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rahul i think u r rite
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2 Dec 2007 20:36:03 IST
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