ComplexListPlot not complete

Question

This code creates three complex lists. The third list is the Union of the other two. There are three plots. When applying ComplexListPlot to all three lists I would expect the third plot to be the first two plots combined. But no! Why? What am I missing?

z = Table[{x, I*y}, {x, -2, 0}, {y, -2, 0}]
s = z^3
g = Union[z, s]
ComplexListPlot[#, Joined -> True, PlotRange -> Full] & @@ z
ComplexListPlot[#, Joined -> True, PlotRange -> Full] & @@ s
ComplexListPlot[#, Joined -> True, PlotRange -> Full] & @@ g

So I expected to add the first and second plot. But The second plot equals the third plot. ComplexListPlot[#, Joined -> True, PlotRange -> Full] & @@ g[[3;;4]] gives partly the right picture. Very strange! I use Mathematica 12.1.

Answer 1

Look at the output from Table. E.g. z

{{{-2, -2 I}, {-2, -I}, {-2, 0}}, {{-1, -2 I}, {-1, -I}, {-1, 0}}, {{0, -2 I}, {0, -I}, {0, 0}}}

This is a list of 3 elements. Each element is a list of tuples. Each tuple contains a real and an imaginary number.

I assume that you wanted to create a list of complex numbers and to plot them. To do so, you must write:

z = Flatten[Table[{x + I*y}, {x, -2, 0}, {y, -2, 0}], 1]

Further, ComplexListPlot takes one argument and options. But when you write

ComplexListPlot[#, Joined -> True, PlotRange -> Full] & @@ z

All the elements of z are given as arguments to ``ComplexListPlot`. The first is then treated as data, the rest as options. Therefore, you should write something like:

z = Flatten[Table[{x + I*y}, {x, -2, 0}, {y, -2, 0}], 1]
s = z^3
g = Union[z, s]
ComplexListPlot[z]
ComplexListPlot[s]
ComplexListPlot[g]