已知复数z=2+i，则z2-2zz-1=（）A.12+32iB.-12-32iC.-12-12iD.12+12i

Question

已知复数z=2+i，则

(z2-2z)/(z-1)=（　　）

A.

(1)/(2)+(3)/(2)i

B. -

(1)/(2)-(3)/(2)i

C. -

(1)/(2)-(1)/(2)i

D.

(1)/(2)+(1)/(2)i

Answer 1

∵复数z=2+i，∴z²-2z=（2+i）²-2（2+i）=3+4i-4-2i=-1+2i，
则(z2-2z)/(z-1)=(-1+2i)/(2+i-1)=((-1+2i)(1-i))/((1+i)(1-i))=(1+3i)/(2)=(1)/(2)+(3)/(2)i．
故选：A．