The graph below depicts the Riemann surface associated with the mapping of the complex number z to w, where z and w fit the relation

z = Aw3 + Bw2 + Cw + D

and the coefficients A, B, C, and D are complex numbers. The real and imaginary parts of these coefficients can be set with the text boxes below.

Ar = Ai =
Br = Bi =
Cr = Ci =
Dr = Di =

The horizontal plane represents the complex domain z. The height of the surface and it color represent the real and imaginary parts of w, respectively. The button switches this relationship.

Use the mouse to control your view of the graph.

Adjust the window for the domain and range below:
zRe min = max =
zIm min = max =
wRe min = max =
wIm min = max =