Plot Complex Lines with mathematica

Question

z1=a;
z2=b;
z3=c;
z[t_]=z1+(z2-z1)t;
z[t_]=z1+(z3-z1)t;
z[t_]=z2+(z3-z2)t;

I want to plot these lines with Mathematica on Unit circle. What will I do?

Answer 1

You could do something like this:

(*Represent your complexes as vectors*)

z1 = {5, 3};
z2 = {.5, .1};
z3 = {-.1, .25};
za[t_] = z1 + (z2 - z1) t;
zb[t_] = z1 + (z3 - z1) t;
zc[t_] = z2 + (z3 - z2) t;  

(*Find the parameter boundaries*)
s = t /. Union[Solve[Norm[za[t]] == 1, t], 
               Solve[Norm[zb[t]] == 1, t],
               Solve[Norm[zc[t]] == 1, t]
         ];

(*And Plot*)
Show[ParametricPlot[{za[t], zb[t], zc[t]}, {t, Min[s], Max[s]}, 
                     RegionFunction -> Function[{x, y}, x^2 + y^2 < 1], 
                     PlotRange -> {{-1, 1}, {-1, 1}}], 
     Graphics@Circle[]
]