# Plot the characteristic roots of complex equation

I want to draw the following pictures as plots in the TikZ environment. The first one is the characteristic roots of the equation

\lambda + \mathrm{e}^{-\lambda}


and the second one is the characteristic roots of the equation

1 + 0.5 \mathrm{e}^{-0.5 \lambda}


• 4th question: tex.meta.stackexchange.com/questions/228 May 1 '18 at 13:35
• pgfplots is the solution to you problem. You can provide a MWE with a specific question if it's not working after looking at related questions and the manual. Here are many examples: pgfplots.sourceforge.net/gallery.html May 1 '18 at 13:37
• Honestly, I think that you are confusing LaTeX with a computer algebra system. You could compute the polylog with an external program and then use pgfplots for visualization, but if you expect pgfplots to know polylogs then I think you need to wait a few years. You could do it with contour plot using gnuplot, though.
– user121799
May 1 '18 at 15:52

This code can be a starting point for you.

\documentclass[a4paper,12pt]{article}
\usepackage{pgfplots}
\begin{document}

\begin{tikzpicture}
\begin{axis}[
ymin = -10,
ymax = 30,
xmin = -5,
xmax = 2,
axis x line=center,
axis y line=center,
]