[tex]z=a+bi\\
|z|=1=\ \textgreater \ \sqrt{a^2+b^2} =1=\ \textgreater \ a^2+b^2=1\\
\displaystyle \frac{z-1}{z+1} = ^{(a+1)-bi)}\frac{(a-1)+bi}{(a+1)+bi} =\\
= \frac{a^2-1+abi+bi-abi+bi+b^2}{a^2+2a+1+b^2}=\\
= \frac{2bi}{2(a+1)} = \frac{b}{a+1}i \in C-R [/tex]
