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Byju's Answer
Standard XII
Mathematics
nth Root of a Complex Number
If 1, ω, ω2 a...
Question
If
1
,
ω
,
ω
2
are three cube roots of unity, then
(
1
−
ω
+
ω
2
)
(
1
+
ω
−
ω
2
)
is
A
1
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B
2
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C
3
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D
4
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Solution
The correct option is
D
4
Since
1
,
ω
,
ω
2
are cube roots of unity,
1
+
ω
+
ω
2
=
0
and
ω
3
=
1
Now,
(
1
−
ω
+
ω
2
)
(
1
+
ω
−
ω
2
)
=
(
−
ω
−
ω
)
(
−
ω
2
−
ω
2
)
=
(
−
2
ω
)
(
−
2
ω
2
)
=
4
ω
3
=
4
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1
Similar questions
Q.
If
1
,
ω
,
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are the three cube roots of unity, then
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)
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.
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If
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−
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+
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)
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