Question

若i为虚数单位，则

(1+2i)2

1-i

-

(2-i)2

1+i

等于（　　）

A．3-4i

B．-3+4i

C．3+4i

D．-3-4i

Answer 1

∵

(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．