Coloring in ComplexListPlot

I want to plot the points of a complex sequence with colors changing from point to point. I tried

ComplexListPlot[  Table[Labeled[1 - 1/(1 + I)^n, Subscript[z, n]], {n, 1, 15}],   AxesLabel -> {"Re(z)", "Im(z)"}, PlotRange -> All,   GridLines -> Automatic,   AxesStyle -> Directive[Black, Arrowheads[{0.0, 0.03}]],   PlotStyle -> ColorData["Rainbow"]] 

I can’t see a change in the color of the points. What am I doing wrong?