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


Re: real parts of powers
Posted:
Feb 14, 2014 6:23 PM


Revised version ...
Warmup problem (not hard):
Show that there exists a complex number c such that both Re(c^n) and Im(c^n) are 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.
Conjecture:
There does not exist a complex number c such that both Re(c^n) and Im(c^n) are 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.
quasi

