Question

Sa se arate ca numarul (cos pi/4 + i sin pi/4)^100 este real.

Answer 1

(cos$(cos\frac{ \pi }{4} +isin \frac{ \pi \pi }{4} ) ^{100}=cos \frac{100 \pi }{4}+isin \frac{100 \pi }{4}=cos25 \pi +isin25 \pi =$$cos \pi +isin \pi =-1$ ∈ R.
$[r(cos \alpha +isin \alpha )]^n=r^n(cosn \alpha +isinn \alpha ) !!!$