若z=-1+(1+i1−i)2011，则z=．

Question

若z=-1+((1+i)/(1−i))2011，则z=______．

Answer 1

∵(1+i)/(1−i)＝((1+i)2)/((1−i)(1+i))=i，i²=-1，i⁴=1．
∴z=-1+i²⁰¹¹=-1+（i⁴）⁵⁰²•i³=-1-i．
故答案为：-1-i．