Question

设i为虚数单位，则1+i+i²+i³+i⁴+i⁵+i⁶=______．

Answer 1

因为i²=-1，所以1+i+i²+i³+i⁴+i⁵+i⁶=1+i-1+i（i²）+（i²）²+i（i⁴）+（i²）³
=1+i-1-i+1+i-1=i．
故答案为i．