z≠1 and z2z−1 is real so imaginary Part is 0
Lets say z=x+iy
So expression =(x+iy)2x+iy−1=x2−y2+2ixy(x−1)+iy
Rationalisation →x2−y2+2ixy(x−1)+iy×(x−1)−iy(x−1)−iy
=(x2−y2+2ixy)((x−1)−iy)(x−1)2+y2
(Imaginary Part =0)⇒2xy(x−1)−x2y+y3=0
⇒2x2y−2xy−x2y+y3=0
⇒x2y+y3−2xy=0
⇒y(x2+y2−2x)=0
⇒y=0 or x2+y2−2x=0
⇒Real axis Line:y=0orCircle:x2+y2−2x=0⇒(x−1)2+(y−0)2=12