问题 选择题
若i为虚数单位,则
(1+2i)2
1-i
-
(2-i)2
1+i
等于(  )
A.3-4iB.-3+4iC.3+4iD.-3-4i
答案

(1+2i)2
1-i
=
(1+2i)2(1+i)
(1-i)(1+i)
=
(-3+4i)(1+i)
2
=
-7+i
2

(2-i)2
1+i
=
(2-i)2(1-i)
(1-i)(1+i)
=
-1-7i
2

(1+2i)2
1-i
-
(2-i)2
1+i

=

-7+i
2
-
-1-7i
2

=-3+4i.

故选B.

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