If n is a positive integer greater than unity and  z is a complex satisfying the equation zn=(z+1)n, then

zn=(z+1)n⇒|z|n=|z+1|n  or  |z|=|z+1|. So the distance of a point z remain same from (0,0) and (–1,0).So ,z lies on perpendicular bisector of line joining (0,0) and (–1,0).that is on x=−12