Question

ARATATI CA 1+i+ i la puterea a 2+ ...+i la puterea a 10=i

Answer 1

Răspuns:

ASA este!!!

Explicație pas cu pas:

1+i+i²+i^10= (1-i^11)/(1-i)=(1-(-i)/(1-i) =(1+i)/(1-i)= (1+i)²/(1-i²)=(1+2i+i²) (1-(-1)) =

(1+2i-1)/(1+1)=2i/2=i

altfel

1+i+i²+i³=0

i^4+...+i^7=0

i^8+i^9+i^10=1+i-1=i

toat suma=i

Answer 2

1+i+i²+i³+...+i^10 =

= 1+i²+i⁴+...+i^10 +

+i+i³+i^5+i^7+i^9 =

= (1+i²)+i⁴(1+i²)+i^8(1+i²)+

i+i³(1+i²)+i^7(1+i²) =

= (1-1)+i⁴(1-1)+i^8(1-1)+i+i³(1-1)+i^7(1-1) = 0+0+0+i+0+0 = i