Question

已知i是虚数单位，则1+i+i2+i3+…i2013的值为______

已知i是虚数单位，则1+i+i2+i3+…i2013的值为______．

Answer 1

∵i²=-1，i⁴=1．
∴1+i+i²+i³+…i²⁰¹³=

1?i2014

1?i

=

1?i2

1?i

=

2

1?i

=

2(1+i)

(1?i)(1+i)

=1+i．
故答案为：1+i．