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Mathematics
Mathematics
Problem
If
1
,
ω
,
ω
2
,
…
,
ω
n
−
1
1, \omega, \omega^2, \dots, \omega^{n-1}
1
,
ω
,
ω
2
,
…
,
ω
n
−
1
are
n
n
n
th roots of unity, find the value of
(
9
−
ω
)
(
9
−
ω
2
)
…
(
9
−
ω
n
−
1
)
(9 - \omega)(9 - \omega^2) \dots (9 - \omega^{n-1})
(
9
−
ω
)
(
9
−
ω
2
)
…
(
9
−
ω
n
−
1
)
.
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