Basically you are facing the problem described here. The simplest workaround is to evaluate
SetOptions[$FrontEndSession, PrintingStyleEnvironment -> "Working"]
before exporting. Now it works as expected:
ComplexListPlot[{0.4 + 0.2 I}, PlotMarkers -> {{Graphics[Triangle[{{{0, 0}, {1, 1.6}, {2, 0}}}]], 0.03}}]; Export["test.pdf", %] // SystemOpen

Note however that your plot marker is misplaced:
Show[ComplexListPlot[{0.4 + 0.2 I}, PlotMarkers -> {{Graphics[Triangle[{{{0, 0}, {1, 1.6}, {2, 0}}}]], 0.2}}], ComplexListPlot[{0.4 + 0.2 I}, PlotStyle -> Red]]

You see that the center of the triangle is misplaced. Here is a way to place your plot marker correctly:
marker = Triangle[{{{0, 0}, {1, 1.6}, {2, 0}}}]; markerCentroid = RegionCentroid[marker]; markerBounds = RegionBounds[yourMarker]; markerPlotRange = Transpose[{markerCentroid - #, markerCentroid + #} &[ Max /@ Abs[markerBounds - markerCentroid]]]; pl = Show[ ComplexListPlot[{0.4 + 0.2 I}, PlotMarkers -> {{Graphics[marker, PlotRange -> markerPlotRange, PlotRangePadding -> 1], 0.5}}], ComplexListPlot[{0.4 + 0.2 I}, PlotStyle -> Red]]

This plot will export correctly even with the default settings for PrintingStyleEnvironment:
SetOptions[$FrontEndSession, PrintingStyleEnvironment -> Inherited] Export["test.pdf", pl] // SystemOpen

Another method is to apply the AlignmentPoint option:
marker = Triangle[{{{0, 0}, {1, 1.6}, {2, 0}}}]; markerCentroid = RegionCentroid[marker]; Show[ComplexListPlot[{0.4 + 0.2 I}, PlotMarkers -> {{Graphics[marker, AlignmentPoint -> markerCentroid, PlotRangePadding -> 1], 0.5}}], ComplexListPlot[{0.4 + 0.2 I}, PlotStyle -> Red]]

All these problems can be easily avoided with ResourceFunction["PolygonMarker"]:
SetOptions[$FrontEndSession, PrintingStyleEnvironment -> Inherited] Show[ComplexListPlot[{0.4 + 0.2 I}, PlotMarkers -> {Graphics[ ResourceFunction["PolygonMarker"]["Triangle", Scaled[0.2]]]}], ComplexListPlot[{0.4 + 0.2 I}, PlotStyle -> Red]] Export["test.pdf", %] // SystemOpen

ImageResolution). Perhaps you have other ideas? $\endgroup$Export["test.pdf", Rasterize[%, ImageSize -> Full, ImageResolution -> 600]];That created a very crisp image for me $\endgroup$