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Byju's Answer
Standard VIII
Mathematics
Cube Root Using Prime Factorisation
If ω is a c...
Question
If
ω
is a complex cube root of unity, then
225
+
(
3
ω
+
8
ω
2
)
2
+
(
3
ω
2
+
8
ω
)
2
=
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Solution
225
+
(
3
ω
+
8
ω
2
)
2
+
(
3
ω
2
+
8
ω
)
2
⟹
We know,
(
a
+
b
)
2
=
a
2
+
2
a
b
+
b
2
Also,
ω
,
ω
2
are cube roots of unity.
⟹
1
+
ω
+
ω
2
=
0
ω
3
=
1
⟹
225
+
(
3
ω
)
2
+
(
64
ω
4
)
+
48
ω
3
+
9
ω
4
+
64
ω
2
+
48
ω
3
⟹
225
+
ω
2
(
9
+
64
)
+
ω
3
(
48
+
48
)
+
ω
4
(
64
+
9
)
⟹
225
+
ω
2
(
73
)
+
ω
3
(
96
)
+
ω
.
ω
3
(
73
)
⟹
225
+
ω
2
(
73
)
+
1
(
96
)
+
ω
.1
(
73
)
⟹
225
+
73
(
ω
+
ω
2
)
+
96
⟹
225
+
73
(
−
1
)
+
96
⟹
248
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Similar questions
Q.
If '
ω
' is a complex cube root of unity, then
225
+
(
3
ω
+
8
ω
2
)
2
+
(
3
ω
2
+
8
ω
)
2
=
Q.
If
ω
is a non real cube root of unity, then
1
+
2
ω
+
3
ω
2
2
+
3
ω
+
ω
2
+
2
+
3
ω
+
ω
2
3
+
ω
+
2
ω
2
=
Q.
If
ω
is a nonreal cuberoot of unity then
1
+
2
ω
+
3
ω
2
2
+
3
ω
+
ω
2
+
2
+
3
ω
+
ω
2
3
+
ω
+
2
ω
2
is equal to
Q.
If
ω
is a cube root of unity, then
(
3
+
5
ω
+
3
ω
2
)
2
+
(
3
+
3
ω
+
5
ω
2
)
2
is equal to
Q.
If
1
,
ω
,
ω
2
are the cube roots of unity then
(
3
+
3
ω
2
+
5
ω
)
6
−
(
2
+
6
ω
2
+
2
ω
)
3
is equal to
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