GraphicsRow[
{ComplexPlot3D[ChebyshevT[1,z],{z,-2-2I,2+2I}], ComplexPlot3D[ChebyshevT[2,z],{z,-2-2I,2+2I}], ComplexPlot3D[ChebyshevT[3,z],{z,-2-2I,2+2I}], ComplexPlot3D[ChebyshevT[4,z],{z,-2-2I,2+2I}], ComplexPlot3D[ChebyshevT[5,z],{z,-2-2I,2+2I}], ComplexPlot3D[ChebyshevT[6,z],{z,-2-2I,2+2I}], ComplexPlot3D[ChebyshevT[7,z],{z,-2-2I,2+2I}], ComplexPlot3D[ChebyshevT[8,z],{z,-2-2I,2+2I}, PlotLegends->Automatic]}]

g = GraphicsRow[{ComplexPlot3D[ChebyshevT[2,z],{z,-1.5-1.5 I,1.5+1.5 I},ColorFunction->"CyclicLogAbs",ScalingFunctions->"Log",ViewPoint->{1,-2.4,0.8}, PlotLabel-> "(Subscript[T, 2])"],
ComplexPlot3D[ChebyshevT[4,z],{z,-1.5-1.5 I,1.5+1.5 I},ColorFunction->"CyclicLogAbs",ScalingFunctions->"Log",ViewPoint->{1,-2.4,0.8},  PlotLabel-> "(Subscript[T, 4])"],
ComplexPlot3D[ChebyshevT[6,z],{z,-1.5-1.5 I,1.5+1.5 I},ColorFunction->"CyclicLogAbs",ScalingFunctions->"Log",ViewPoint->{1,-2.4,0.8},  PlotLabel-> "(Subscript[T, 6])"],
ComplexPlot3D[ChebyshevT[8,z],{z,-1.5-1.5 I,1.5+1.5 I},ColorFunction->"CyclicLogAbs",ScalingFunctions->"Log",ViewPoint->{1,-2.4,0.8}, PlotLabel-> "(Subscript[T, 8])"],
ComplexPlot3D[ChebyshevT[10,z],{z,-1.5-1.5 I,1.5+1.5 I},ColorFunction->"CyclicLogAbs",ScalingFunctions->"Log",ViewPoint->{1,-2.4,0.8}, PlotLabel-> "(Subscript[T, 10])"]}, ImageSize->1000]

Export["~/Downloads/complex_chebyshev.png", g, Background->None, ImageResolution->200]

g2 = ComplexPlot3D[ChebyshevT[10,z],{z,-1.5-1.5 I,1.5+1.5 I},ColorFunction->"CyclicLogAbs",ScalingFunctions->"Log",ViewPoint->{1,-2.4,0.8}, PlotLabel-> "(Subscript[T, 10])", PlotLegends->Automatic]

Export["~/Downloads/bar.png", g2, Background->None, ImageResolution->200]