complex operator/ (const complex& c1, const complex& c2)
{
double abs2c2 = c2.abs2();
double res_re = (c1.get_re()*c2.get_re() + c1.get_im()*c2.get_im())/abs2c2;
double res_im = (c1.get_im()*c2.get_re() - c1.get_re()*c2.get_im())/abs2c2;
complex res{res_re, res_im};
return res;
}
//Construct the line with a given center
line::line(complex center){
left = ideal(complex(1.0, sqrt(center.abs2() - 1.0)) / center.conj());
right = ideal(complex(1.0, -sqrt(center.abs2() - 1.0)) / center.conj());
}