Explicație pas cu pas:
i²=-1, i⁴=1
i+i²+i³+...+i¹⁰⁰= (i+i²+i³+i⁴)+(i⁵+i⁶+i⁷+i⁸)+...+(i⁹⁷+i⁹⁸+i⁹⁹+i¹⁰⁰)=(i+i²+i³+i⁴)(1+i⁴+i⁸+i¹²+...+i⁹⁶)= [i+(-1) +(-i)+ 1] •(...)= (i-i+1-1) •(...)= 0• (...)=0
