Assuming we have to plot Log[Abs[h[v]]] (Thanks @user64494 's comment)
Try DensityPlotand Plot3D:
DensityPlot[Evaluate@Log[Abs[h[vre + I vim]]], {vre, 0, 10},{vim, -10, 0 },ColorFunction -> Hue, ColorFunctionScaling -> False] 
Plot3D[Evaluate@Log[Abs[h[vre + I vim]]], {vre, 0, 10}, {vim,-10,0 }, AxesLabel -> {"Re[v]", "Im[v]", "Log[Abs[h[v ]]]"},ColorFunction -> Hue, MeshFunctions -> {#3 &}] 
Assuming we have to plot Log[Abs[h[v]]] (Thanks @user64494 's comment)
Try DensityPlotand Plot3D:
DensityPlot[Evaluate@Log[Abs[h[vre + I vim]]], {vre, 0, 10},{vim, -10, 0 },ColorFunction -> Hue, ColorFunctionScaling -> False]
Plot3D[Evaluate@Log[Abs[h[vre + I vim]]], {vre, 0, 10}, {vim,-10,0 }, AxesLabel -> {"Re[v]", "Im[v]", "Log[Abs[h[v ]]]"},ColorFunction -> Hue, MeshFunctions -> {#3 &}]
Assuming we have to plot Log[Abs[h[v]]] (Thanks @user64494 's comment)
Try DensityPlotand Plot3D:
DensityPlot[Evaluate@Log[Abs[h[vre + I vim]]], {vre, 0, 10},{vim, -10, 0 },ColorFunction -> Hue, ColorFunctionScaling -> False]
Plot3D[Evaluate@Log[Abs[h[vre + I vim]]], {vre, 0, 10}, {vim,-10,0 }, AxesLabel -> {"Re[v]", "Im[v]", "Log[Abs[h[v ]]]"},ColorFunction -> Hue, MeshFunctions -> {#3 &}]
Assuming we have to plot Log[Abs[h[v]]] (Thanks @user64494 's comment)
Try DensityPlotand Plot3D:
DensityPlot[Evaluate@Abs[Log[h[vreDensityPlot[Evaluate@Log[Abs[h[vre + I vim]]], {vre, 0, 10},{vim, -10, 0 },ColorFunction -> Hue, ColorFunctionScaling -> False] 
Plot3D[Evaluate@Abs[Log[h[vrePlot3D[Evaluate@Log[Abs[h[vre + I vim]]], {vre, 0, 10}, {vim,-10,0 }, AxesLabel -> {"Re[v]", "Im[v]", "Abs[Log[h[v"Log[Abs[h[v ]]]"},ColorFunction -> Hue, MeshFunctions -> {#3 &}] 
Try DensityPlotand Plot3D:
DensityPlot[Evaluate@Abs[Log[h[vre + I vim]]], {vre, 0, 10},{vim, -10, 0 },ColorFunction -> Hue, ColorFunctionScaling -> False]
Plot3D[Evaluate@Abs[Log[h[vre + I vim]]], {vre, 0, 10}, {vim,-10,0 }, AxesLabel -> {"Re[v]", "Im[v]", "Abs[Log[h[v ]]]"},ColorFunction -> Hue, MeshFunctions -> {#3 &}]
Assuming we have to plot Log[Abs[h[v]]] (Thanks @user64494 's comment)
Try DensityPlotand Plot3D:
DensityPlot[Evaluate@Log[Abs[h[vre + I vim]]], {vre, 0, 10},{vim, -10, 0 },ColorFunction -> Hue, ColorFunctionScaling -> False]
Plot3D[Evaluate@Log[Abs[h[vre + I vim]]], {vre, 0, 10}, {vim,-10,0 }, AxesLabel -> {"Re[v]", "Im[v]", "Log[Abs[h[v ]]]"},ColorFunction -> Hue, MeshFunctions -> {#3 &}]
Try DensityPlotand Plot3D:
DensityPlot[Evaluate@Abs[Log[h[vre + I vim]]], {vre, 0, 10},{vim, -10, 0 },ColorFunction -> Hue, ColorFunctionScaling -> False]
Plot3D[Evaluate@Abs[Log[h[vre + I vim]]], {vre, 0, 10}, {vim,-10,0 }, AxesLabel -> {"Re[v]", "Im[v]", "Abs[Log[h[v ]]]"},ColorFunction -> Hue, MeshFunctions -> {#3 &}]
Try
Plot3D[Evaluate@Abs[Log[h[vre + I vim]]], {vre, 0, 10}, {vim,-10,0 }, AxesLabel -> {"Re[v]", "Im[v]", "Abs[Log[h[v ]]]"},ColorFunction -> Hue, MeshFunctions -> {#3 &}]
Try DensityPlotand Plot3D:
DensityPlot[Evaluate@Abs[Log[h[vre + I vim]]], {vre, 0, 10},{vim, -10, 0 },ColorFunction -> Hue, ColorFunctionScaling -> False]
Plot3D[Evaluate@Abs[Log[h[vre + I vim]]], {vre, 0, 10}, {vim,-10,0 }, AxesLabel -> {"Re[v]", "Im[v]", "Abs[Log[h[v ]]]"},ColorFunction -> Hue, MeshFunctions -> {#3 &}]