Byju's Answer
Standard XII
Mathematics
Cube Root of a Complex Number
If ω is a cub...
Question
If
ω
is a cube root of unity, then
(
1
+
ω
)
3
−
(
1
+
ω
2
)
3
=
A
0
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B
ω
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C
ω
2
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D
None of these
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Solution
The correct option is
A
0
(
1
+
ω
)
3
−
(
1
+
ω
2
)
3
=
(
−
ω
2
)
3
−
(
−
ω
)
3
=
−
ω
6
+
ω
3
=
−
ω
3
ω
3
+
ω
3
=
−
1
+
1
=
0
Suggest Corrections
0
Similar questions
Q.
If
ω
is a cube root of unity, then
(
1
+
ω
)
3
−
(
1
+
ω
2
)
3
=
Q.
If
ω
represents a complex cube root of unity, then
(
3
−
ω
)
(
3
−
ω
2
)
(
3
−
ω
4
)
(
3
−
ω
8
)
=
Q.
If 1,
ω
,
ω
2
are the three cube roots of unity, then
(
1
+
ω
)
3
−
(
1
+
ω
2
)
3
=
0.
Q.
If
1
,
ω
,
ω
2
are the cube roots of unity, then the value of
(
3
+
ω
)
(
3
+
ω
2
)
(
3
+
ω
10
)
(
3
+
ω
11
)
is
Q.
1
,
ω
,
ω
2
are the cube roots of unity, then the value of
(
1
+
w
)
3
−
(
1
+
ω
2
)
3
is-
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