（2009•江苏模拟）已知i是虚数单位，计算：(1+2i1−i)2−(2−i1+i)2=．

Question

（2009•江苏模拟）已知i是虚数单位，计算：((1+2i)/(1−i))2−((2−i)/(1+i))2=______．

Answer 1

((1+2i)/(1−i))2−((2−i)/(1+i))2=(((1+2i)(1+i))/((1−i)(1+i)))2−(((2−i)(1−i))/((1+i)(1−i)))2=((−1+3i)/(2))2-((3−3i)/(2))2
=（(1)/(4)-(9)/(4)-(3)/(2) i ）-（-(9)/(2) i ）=-2+3i，
故答案为-2+3i．