Plot Complex Lines with mathematica -

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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 plot these lines mathematica on unit circle. do?

you this: 

(*represent complexes 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 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[] ]

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