\documentclass[margin=.2cm,multi,tikz]{standalone}
\usepackage{luahyperbolic} %loads luacode package
\begin{document}
\begin{luacode*}
hyper.tikzBegin("scale=2.5")
local P = complex(0.5,-0.2)
local A = complex.exp_i(math.pi/10)
for k=1,5 do hyper.drawLine(P, A^k, "teal") end
hyper.labelPoint(P, "$P$", "left=.2cm")
hyper.drawLine(complex.J,-complex.I,"very thick, dashed, red")
hyper.tikzEnd()
\end{luacode*}
\end{document}