Amp(Z+1Z−2i)=π2 then locus of Z = x + iy is

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x2+y2+3x−2=0,y=0

X = 0 such that y > 23

x2+y2+2x−4y=0 such that y < 0, x2+ y2 > 1

x2+y2+x−2y=0 such that 2x – y + 2 > 0

answer is D.

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Detailed Solution

Amp[(x+1)+iyx+i(y−2)]=π2 ⇒Amp xx+1+yy-2+ixy-x+1y-2x2+y-22=π2 ⇒x(x+1)+y(y−2)=0,xy−(x+1)(y−2)>0 i.e 2x – y + 2 > 0 which is the required locus.

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