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AP EAMCET Engineering 2018 Apr 22 Shift 1 Paper
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© examsnet.com
Question : 10
Total: 160
If
1
,
ω
,
ω
2
are the cube roots of unity, then
1
1
+
2
ω
+
1
2
+
ω
−
1
1
+
ω
=
1
ω
ω
2
0
Validate
Solution:
The given equation is.
1
1
+
2
ω
+
1
2
+
ω
−
1
1
+
ω
=
(
3
+
3
ω
)
(
1
+
ω
)
−
(
1
+
2
ω
)
(
2
+
ω
)
(
1
+
2
ω
)
(
2
+
ω
)
(
1
+
ω
)
=
3
+
6
ω
+
3
ω
2
−
2
−
ω
−
4
ω
−
2
ω
2
(
1
+
2
ω
)
(
2
+
ω
)
(
1
+
ω
)
=
1
+
ω
+
ω
2
(
1
+
2
ω
)
(
2
+
ω
)
(
1
+
ω
)
Substitute
1
+
ω
+
ω
2
=
0
in above expression.
1
1
+
2
ω
+
1
2
+
ω
−
1
1
+
ω
=
0
© examsnet.com
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