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Topic: real parts of powers
Replies: 9   Last Post: Feb 15, 2014 1:41 PM

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Posts: 43
Registered: 11/26/09
Re: real parts of powers
Posted: Feb 14, 2014 5:27 PM
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On Friday, February 14, 2014 10:40:36 PM UTC+1, quasi wrote:

> Show that there exists a complex number c such that Re(c^n)
> is nonzero for all positive integers n, and such that
> Re(c^n1) = Re(c^n2) = Re(c^n3) = Re(c^n4)
> where n1,n2,n3,n4 are distinct positive integers.

Maybe I'm missing something.
What about c = -1/2 + I* Sqrt(3)/2, which satisfies c^3 = 1 ?

I think that Re(c^n) = -1/2 for all n which are not multiples of 3 and
Re(c^n)=1 for n=3k.


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