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Mathematics
Mathematics
Problem
If
ω
=
α
+
i
β
\omega = \alpha + i\beta
ω
=
α
+
i
β
, where
β
≠
0
\beta \neq 0
β
=
0
,
i
=
−
1
i = \sqrt{-1}
i
=
−
1
and
z
≠
1
z \neq 1
z
=
1
, satisfies the condition that
(
ω
−
ω
ˉ
z
1
−
z
)
\left(\frac{\omega - \bar{\omega}z}{1 - z}\right)
(
1
−
z
ω
−
ω
ˉ
z
)
is purely real, the set of values of
z
z
z
is a.
{
z
:
∣
z
∣
=
1
}
\{z : |z| = 1\}
{
z
:
∣
z
∣
=
1
}
b.
{
z
:
z
=
z
ˉ
}
\{z : z = \bar{z}\}
{
z
:
z
=
z
ˉ
}
c.
{
z
:
z
≠
1
}
\{z : z \neq 1\}
{
z
:
z
=
1
}
d.
{
z
:
∣
z
∣
=
1
,
z
≠
1
}
\{z : |z| = 1, z \neq 1\}
{
z
:
∣
z
∣
=
1
,
z
=
1
}
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