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.