If `w=alpha+ibeta` where `Beta 0 ` and `z ne 1` satisfies the condition that `((w- bar wz)/(1-z))` is purely real then the set of values of z is

Options

A. `{z:|z|=1}`
B. `{z:z=bar(z)}`
C. `{z:z!=1}`
D. `{z:}|z|=1,z!=1|`

Explanation

If A is purely real then `A=bar(A)`
`:. (omega-bar(omega)z)/(1-z)=(bar(omega)-omega(z))/(bar(z))`
`rArr(zbar(z)-1)(bar(omega)-omega)=0`
`rArrzbar(z)=1[:'bar(omega)=omega` is not possible as `beta!=0]`
`rArr|z|^(2)=1 rArr |z|=1`
`rArr z !=` [since`(omega-bar(omega)z)/(1-z)` is defined if `z!=1`]