If \( \omega=\alpha+i \beta \), where \( \beta \neq 0, i=\sqrt{-1} ...

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If \( \omega=\alpha+i \beta \), where \( \beta \neq 0, i=\sqrt{-1} \) and \( z \neq 1 \), satisfies the condition that \( \left(\frac{\omega-\bar{\omega} z}{1-z}\right) \) is purely real, the set of values
\( \mathrm{P} \)
\( \mathrm{W} \) of \( z \) is
[IIT-JEE 2006, 3M]
(a) \( \{z:|z|=1\} \)
(b) \( \{z: z=\bar{z}\} \)
(c) \( \{z: z \neq 1\} \)
(d) \( \{z:|z|=1, z \neq 1\} \)
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