Question

已知复数z=x+yi(x、y∈R,i是虚数单位)满足不等式z+iz-i≤0(表示复数z的共轭复数),则u=|2x-y+1|的取值范围是

A.［0,+∞)                                    B.［3-,3+］

C.［0,］                                   D.［0,1+］

Answer 1

C  将z=x+yi(x,y∈R)代入zz+iz-iz≤0,整理得x²+(y-1)²≤1,它表示以(0,1)为圆心,以1为半径的圆及圆内的点构成的集合,则圆内任一点P(x,y)到直线2x-y+1=0的距离d=∈［0,1］,∴|2x-y+1|∈［0,］,即u∈［0,］.