for n in the natural numbers prove that (2+i)^n is never real.
(2+i) is not real
for k=n assume (2+i)^k is not in the reals
Ive got to the point where
2(2+i)^k + i(2+i)^k must not be real. its seems logical that the i terms would not cancel out making this sum not real but i cant figure out a way to prove it.
I've tried using the binomial theorem. Any HINTS would be greatly appreciated.