quasi
Posts:
11,765
Registered:
7/15/05


Re: real parts of powers
Posted:
Feb 14, 2014 6:10 PM


giovanni wrote: >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.
No, you're fine.
>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.
Yep  I need a further restriction.
I'll revise the problem in my next reply.
Thanks for making me aware of the issue.
quasi

