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UPSC NDA Math Model Paper 6
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© examsnet.com
Question : 94
Total: 120
Evaluate
(
1
+
ω
−
ω
2
)
8
, where
ω
is cube root of unity.
-256 ω
256 ω
-128 ω
+128 ω
Validate
Solution:
Here, we have to evaluate the expression
(
1
+
ω
−
ω
2
)
8
, where ω is cube root of unity.
As we know that,
1
+
ω
+
ω
2
=
0
⇒
(
1
+
ω
−
ω
2
)
8
=
(
−
ω
2
−
ω
2
)
8
=
(
−
2
ω
2
)
8
=
2
8
ω
16
=
256
ω
.
ω
15
=
256
ω
(
ω
3
)
15
.
.
.
.
.
.
.
.
(
∵
ω
3
=
1
)
=
256
ω
Hence, option
B
is the correct answer.
© examsnet.com
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