(b) हम जानते हैं कि $|{z_1}|\; = 1$ एवं ${z_2}$कोई सम्मिश्र संख्या है

$ \Rightarrow \left| {\;\frac{{{z_1} – {z_2}}}{{1 – {z_1}{{\bar z}_2}}}} \right|\; = \frac{{|{z_1} – {z_2}|}}{{\left| {\;1 – \frac{{{{\bar z}_2}}}{{{{\bar z}_1}}}\;} \right|}}$;  $\because \;{z_1}{\bar z_1} = \;|{z_1}{|^2}$      

$ = \frac{{|{z_1} – {z_2}|}}{{|{{\bar z}_1} – {{\bar z}_2}|}}|{\bar z_1}|$;  दिया है $\because \;|{\bar z_1}|\; = 1$

$ = \frac{{|{z_1} – {z_2}|}}{{|\overline {{z_1} – {z_2}} |}} = \frac{{|{z_1} – {z_2}|}}{{|{z_1} – {z_2}|}} = 1$.