Răspuns:
a) i^{55}
b) [tex]\frac{i^{11} - 1}{i - 1}[/tex]
Explicație pas cu pas:
a) [tex]i*i^{2} *i^{3} * ... *i^{10} =i^{1+2+3+...+10} = i^{\frac{10*11}{2}} = i^{55}[/tex]
b) Fie [tex]S = 1 + i + i^{2} + i^{3} + ... + i^{10}[/tex]
[tex]i*S = i + i^{2} + i^{3} + i^{4} + ... + i^{10} + i^{11}\\\\i*S-S = i+i^{2} +i^{3} +i^{4}+ ...+i^{10}+ i^{11} - (1+i+i^{2} +i^{3} + ...+i^{10})\\i*S-S = i+i^{2} +i^{3} +i^{4}+ ...+i^{10}+ i^{11} - 1-i-i^{2} - i^{3} - ...-i^{10}\\S*(i-1) = i^{11} - 1\\S = \frac{i^{11} - 1}{i-1}[/tex]
