Question

Va rog ajutor rapid


i+i^2+i^3+....+i^10

Answer 1

i+i^2+i^3+....+i^10
i^1+2+3+....+10
i^10*(10+1):2
i^10*11:2
i^5*11
i^55

Answer 2

 i+i^2+i^3+....+i^10

i^2=-1; i^3=i·i^2=-i; i^4=(i^2)^2=1; i^5=i;  i^6=1^2·i^4=-1;  i^7=i·i^6=-i;  i^8=1; i^9=i; i^10=i^2·i^8=-1

=> i+i^2+i^3+....+i^10=i-1-i+1+i-1-i+1+i-1= i-1