quasi
Posts:
12,067
Registered:
7/15/05


Re: real parts of powers
Posted:
Feb 14, 2014 6:19 PM


Zeit Geist wrote: >quasi wrote: >> >>Warmup problem (not hard): >> >>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) >> >>for some distinct positive integers n1,n2,n3. > >Are you asking for a nonreal complex number c?
Not as stated.
But I missed a needed restriction which would have implied that c is nonreal.
>If not, let c = 1. For any even positive integer n, we have >(1)^n = 1. Similarly, for odd n, resulting in 1.
For that matter, c = 1 works.
>ZG > >PS. If I'm completely missing something, please be polite. >Thank you.
Don't be silly  I'm always polite (well, ok, not always, but most of the time, at least when replying to nontrolls).
Thanks for alerting me to the need for a correction.
I'll try again with a revised wording of the problem in my next reply.
quasi

