Question

Комплексные числа. (1+i)^10=?

Answer 1

1+i=sqrt(2)*cosП/4+isqrt(2)sinП/4
r=sqrt(1+1)=sqrt(2)
f=arctg(1)=П/4

(1+i)^10=(sqrt(2))^10(cos10*П/4+isin10п/4)=2^5(cos(2,5П+isin2,5П)=32(сosп/2+isinП/2)=32i