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WBJEE 2016 Math Solved Paper
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© examsnet.com
Question : 62
Total: 75
If ω is an imaginary cube root of unity, then the value of
(2 + ω) (2 -
ω
2
) + 2 (3 - ω) ( 3 -
ω
2
+ ..... + (n-1) (n - ω) ( n -
ω
2
) is
n
2
4
(
n
+
1
)
2
−
n
n
2
4
(
n
+
1
)
2
+
n
n
2
4
(
n
+
1
)
2
n
2
4
(
n
+
1
)
−
n
Validate
Solution:
n
Σ
r
=
2
(r - 1) (r - ω) (r -
ω
2
) =
n
Σ
r
=
2
(
r
3
−
1
)
=
[
n
2
(
n
+
1
)
2
4
−
1
]
- (n - 1) =
n
2
(
n
+
1
)
2
4
- n
© examsnet.com
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