IIT JEE , AIEEE Forum - Mathematics , Algebra

haseeb2009

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

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