1=1
i=i
i²=-1
i³=-i
i^4=1
i^5=i
i^6=-1
i^7=-i
i^8=1
i^9=i
i^10=-1
____________________
1+i+...+i^10=1-1-i+1+i-1-i+1+i-1=3-3+2i-2i=0