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Byju's Answer
Standard XII
Mathematics
Binomial Theorem
a + bω + cω 2...
Question
(
a
+
b
ω
+
c
ω
2
c
+
a
ω
+
b
ω
2
)
+
(
a
+
b
ω
+
c
ω
2
b
+
c
ω
+
a
ω
2
)
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Solution
As we know that
ω
3
=
1
,
1
+
ω
+
ω
2
=
0
(
a
+
b
ω
+
c
ω
2
c
+
a
ω
+
b
ω
2
)
+
(
a
+
b
ω
+
c
ω
2
b
+
c
ω
+
a
ω
2
)
=
(
a
ω
3
+
b
ω
4
+
c
ω
2
c
+
a
ω
+
b
ω
2
)
+
(
a
ω
3
+
b
ω
+
c
ω
2
b
+
c
ω
+
a
ω
2
)
=
(
ω
2
)
×
(
c
+
a
ω
+
b
ω
2
c
+
a
ω
+
b
ω
2
)
+
(
ω
)
×
(
b
+
c
ω
+
a
ω
2
b
+
c
ω
+
a
ω
2
)
=
ω
+
ω
2
=
−
1
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0
Similar questions
Q.
The value of
a
+
b
ω
+
c
ω
2
b
+
c
ω
+
a
ω
2
+
a
+
b
ω
+
c
ω
2
c
+
a
ω
+
b
ω
2
will be
Q.
If
ω
is a complex cube root of unity, the the value of
a
+
b
ω
+
c
ω
2
c
+
a
ω
+
b
ω
2
+
a
+
b
ω
+
c
ω
2
b
+
c
ω
+
a
ω
2
Q.
If cube root of unity is
1
,
ω
,
ω
2
then find the value of:
(
a
+
b
ω
+
c
ω
2
)
(
c
+
a
ω
+
b
ω
2
)
+
(
a
+
b
ω
+
c
ω
2
)
(
b
+
c
ω
+
a
ω
2
)
Q.
Find the value of the given expression:
a
+
b
ω
+
c
ω
2
c
+
a
ω
+
b
w
2
+
a
+
b
ω
+
c
ω
2
b
+
c
ω
+
a
ω
2
Q.
If
ω
is a cube root of unity, and the value of
(
1
−
ω
)
(
1
−
ω
2
)
(
1
−
ω
4
)
(
1
−
ω
8
)
=
α
,
and
a
+
b
ω
+
c
ω
2
b
+
c
ω
+
a
ω
2
+
a
+
b
ω
+
c
ω
2
c
+
a
ω
+
b
ω
2
=
β
then
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