If \( \frac{w-\bar{w} z}{1-z} \) is purely real where \( w=\alpha+i \beta, \beta \neq 0 \) and \...

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If \( \frac{w-\bar{w} z}{1-z} \) is purely real where \( w=\alpha+i \beta, \beta \neq 0 \) and \( z \neq 1 \), then the set of the values of \( z \) is
(A) \( \{z:|z|=1\} \)
(B) \( \{z: z \neq 1\} \)
(C) \( \{z: z=\bar{z}\} \)
(D) \( \{z:|z|=1, z \neq 1\} \)
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