Assuming we have to plot `Log[Abs[h[v]]]` (Thanks @user64494 's comment) 

Try `DensityPlot`and `Plot3D`:

 DensityPlot[Evaluate@Log[Abs[h[vre + I vim]]], {vre, 0, 10},{vim, -10, 0 },ColorFunction -> Hue, ColorFunctionScaling -> False]

[![enter image description here][1]][1]


 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 &}]

 [![enter image description here][2]][2]


 [1]: https://i.sstatic.net/kEFwo.png
 [2]: https://i.sstatic.net/PfpnU.png