Question

已知i是虚数单位，m∈R，且

2-mi

1+i

是纯虚数，则(

2-mi

2+mi

)2011=______．

Answer 1

因为

2-mi

1+i

=

(2-mi)(1-i)

2

=

(2-m)-(2+m)i

2

是纯虚数，所以m=2．
故(

2-mi

2+mi

)2011=(

2-2i

2+2i

)2011=（-i）²⁰¹¹ =-i³ =i．
故答案为：i．