Show the geometric representation of the.... (elementary algebra)

Question

Show the geometric representation of the set {z∈C| |z+1| =5}

Answer 1

If z=x+yi then z+1=(x+1)+yi, and the representation of |z+1|=5 is the circle (x+1)^2+y^2=25, a circle radius 5 which, as a graph would be centred at (-1,0). The set of all z would be the set of all points on the circumference, where the real component of z is displaced by 1. z would be the set of points on the circumference of the circle as measured from the origin (0,0).