Question

Комплексные числа. (1+i)^10=?

Answer 1

(1+i)^10=?
!z!=√1²+1²=√2
1+i=√2(cosπ/4+isinπ/4)
z^n=!z!^n(cos n*a+isin n*a)
(1+i)^10=(√2)^10(cos 10*π/4 +i sin 10*π/4)=(√2)^10(cos 5π/2+i sin 5π/2)