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 non-real complex number c?
Not as stated.
But I missed a needed restriction which would have implied that c is non-real.
>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 non-trolls).
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.