prove-that-1-i-n-1-i-n-2-n-1-2-

Question Number 138362 by mohammad17 last updated on 12/Apr/21

p r o v e t h a t

{(1 + i)}^{n} + {(1 - i)}^{n} = 2^{\frac{n + 1}{2}}

Commented by Dwaipayan Shikari last updated on 12/Apr/21

{(1 + i)}^{n} + {(1 - i)}^{n}

= 2^{\frac{n}{2}} e^{\frac{π n}{4} i} + 2^{\frac{n}{2}} e^{\frac{- π n}{4} i}

= 2^{\frac{n}{2} + 1} c o s (\frac{π n}{4})