Thanks in advance for any helpExplain why $\displaystyle z = (1 + i)^n + (1 - i)^n$ is real for all $\displaystyle n \in N$
Finally, you could do this using the binomial theorem, together with the fact that $\displaystyle \left(\begin{array}{c}n \\ k\end{array}\right)= \left(\begin{array}{c}n \\ n-k \end{array}\right)$, and combining all odd powers of i.