\documentclass[margin=.2cm,multi,tikz]{standalone}
\usepackage{../luahyperbolic}
\begin{document}
\begin{luacode*}
local N = 30

hyper.tikzBegin()
for k=1,N-1 do
	local P = complex.exp_i(k*math.pi/N)
	hyper.drawLine(P,complex.conj(P),"red")
end
hyper.tikzEnd()

-- second image :

hyper.tikzBegin()
for k=1,N-1 do
local P = complex.exp_i(2*k*math.pi/N)
hyper.drawLine(P,1,"teal")
end
hyper.tikzEnd()

-- third image:

local Omega = 0.2+0.3*complex.I
hyper.tikzBegin()
for k=0,N-1 do
	local v = complex.exp_i(2*k*math.pi/N)
	hyper.drawLineFromVector(Omega,v,"blue")
end
hyper.tikzEnd()

\end{luacode*}
\end{document}