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Byju's Answer
Standard XIII
Mathematics
Cube Root of a Complex Number
If ω is a cub...
Question
If
ω
is a cube root of unity, then
(
1
+
ω
−
ω
2
)
(
1
−
ω
+
ω
2
)
=
[MNR 1990; MP PET 1993, 2002]
A
1
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B
0
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C
2
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D
4
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Solution
The correct option is
D
4
If
ω
is a complex cube root of unity then
ω
3
=
1
and
1
+
ω
+
ω
2
=
0
,
therefore
(
1
+
ω
−
ω
2
)
(
1
−
ω
+
ω
2
)
=
(
−
2
ω
2
)
(
−
2
ω
)
=
4
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0
Similar questions
Q.
If
ω
is a cube root of unity, then
(
1
+
ω
−
ω
2
)
(
1
−
ω
+
ω
2
)
=
[MNR 1990; MP PET 1993, 2002]
Q.
If
1
,
ω
,
ω
2
are three cube roots of unity, then
(
1
−
ω
+
ω
2
)
(
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+
ω
−
ω
2
)
is
Q.
If
ω
is a cube root of unity.
Find
(
1
+
ω
−
ω
2
)
(
1
−
ω
+
ω
2
)
Q.
If
ω
being the cube root of unity then find the value of
(
1
−
ω
+
ω
2
)
(
1
+
ω
−
ω
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)
.
Q.
If
ω
is one of the complex cube roots of unity, then
(
1
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