This is a classical problem, posed by one time cattle herder, Thomas Clausen in 1827. ( This is not one of those quaint ones where a cancellation of zeros occur).Note : Click on the image to see it in enlarged form.
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I am sure its a result of problem in the statement exp(2*pi*i)^(2*pi*i) = exp (-4pi^2)
ReplyDeleteBut should actually be 1. But I do not know the rules involving powers of powers in complex number. Please enlighten.
also it this statement seems wierd..
exp(2*pi*i)^(2*pi) should be 1, but
again it can also be exp(4*pi^2*i) which is not 1.
on the hindsight of our discussion, z^(2*pi) - exp(4*pi^2*i) = 0 has 1 as a root.
ReplyDeleteThat's actually the catch in this problem.