Let's look at solutions to x2+y2 = 1 for x and y complex.

Move the slider below to set the value of one of Re(x), Im(x), Re(y), or Im(y) (choose which one using the drop down menu) to see a portion of that cross-section of the 3d shape in 4d. Check the "Show Projection" box below to see all these cross sections unioned together. There may be artifacts due to the way points are sampled.



Show Projection (union of all cross sections)
Auto-rotate around conjugate axis
Show hypersphere of radius
Show and label axes