Hence the horizontal plane contains the Re(x) ([equivalent to] G) and Im(x) ([equivalent to] H) axes, thus forming the Argand plane, whilst the vertical plane given by GA or GB represents the Cartesian plane for each surface.

With reference to Figures 3(d) and 4(d), when viewed from above, Surfaces A and B both share a common umbilical point located in the Argand plane at G = -1, H = 0.

The roots are represented in the Argand plane by points that lie equally pitched around a circle of unit radius.

n] - 1 in the Cartesian plane and the resulting n-roots which invariably appear in the Argand plane.

This approach is much simpler than the comprehensive analysis presented by Bardell (2012, 2014), but it does not make the full visual connection between the Cartesian plane and the Argand plane that Bardell's three dimensional surfaces illustrated so well.

5i as plotted in Figure 1 are effectively translated by an amount -b/2a in the Argand plane as the final part of the solution process; the point -b/2a locates the new centre of the circle.

In the three-dimensional surfaces that follow, the horizontal plane contains the Re(x) ([equivalent to] G) and Im(x) ([equivalent to] H) axes, thus forming the

Argand plane, whilst the vertical axis represents either Re(y) ([equivalent to] A) or Im(y) ([equivalent to] B) depending on which surface is being investigated.

In the 3D surfaces that follow, the horizontal plane contains the Re(x) ([equivalent to] G) and Im(x) ([equivalent to] H) axes, thus forming the

Argand plane, whilst the vertical axis represents either Re(y) ([equivalent to] A) or Im(y) ([equivalent to] B) depending on which surface is being investigated.