Question

i为虚数单位，则（1+i1?i）2014等于______

i为虚数单位，则（1+i1?i）2014等于______．

Answer 1

∵

1+i

1?i

=

(1+i)2

(1?i)(1+i)

=

2i

2

=i，
∴则（

1+i

1?i

）²⁰¹⁴=i²⁰¹²?i²=-1．
故答案为：-1．