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Byju's Answer
Standard XII
Mathematics
nth Root of a Complex Number
If 1, ω, ω2...
Question
If
1
,
ω
,
ω
2
are the cube roots of unity, then prove that
(
2
−
ω
)
(
2
−
ω
2
)
(
2
−
ω
10
)
(
2
−
ω
11
)
=
49
Open in App
Solution
Given
1
,
ω
,
ω
2
are the cube roots of unity
⟹
1
+
ω
+
ω
2
=
0
,
ω
3
=
1
L
H
S
=
(
2
−
ω
)
(
2
−
ω
2
)
(
2
−
ω
10
)
(
2
−
ω
11
)
=
(
2
−
ω
)
(
2
−
ω
2
)
(
2
−
(
ω
3
)
3
ω
)
(
2
−
(
ω
3
)
3
ω
2
)
=
(
(
2
−
ω
)
(
2
−
ω
)
2
)
2
=
(
2
2
−
2
(
ω
+
ω
2
)
+
ω
3
)
2
=
(
4
+
2
+
1
)
2
=
7
2
=
49
=
R
H
S
Hence proved
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Q.
If
1
,
ω
,
ω
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are the cube roots of unity then the value of
(
2
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2
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(
2
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(
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Q.
If
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,
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Q.
1
,
ω
,
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2
are the cube roots of unity then
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2
−
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−
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2
)
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