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

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.