∵Z= 1 i?1 = ?1?i (?1+i)(?1?i) = ?1?i 2 =? 1 2 ? 1 2 i,∴复数Z= 1 i?1 的模为 (? 1 2 )2+(? 1 2 )2 = 2 2 .故答案为: 2 2 .