Question

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．