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UPSC NDA II 2011 Mathematics Paper
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© examsnet.com
Question : 1
Total: 120
What is the value of
(
1
+
i
)
5
+
(
1
−
i
)
5
where
i
=
√
−
1
?
−
8
8
8
i
−
8
i
Validate
Solution:
(
1
+
i
)
5
+
(
1
−
i
)
5
=
1
+
5
c
1
1
4
⋅
i
+
5
c
2
(
1
)
3
(
i
)
2
+
5
c
3
(
1
)
2
(
i
)
3
+
5
c
4
(
1
)
(
i
)
4
+
i
5
+
1
−
5
c
1
(
1
)
4
i
+
5
c
2
(
1
)
3
⋅
(
i
)
2
−
5
c
3
(
1
)
2
i
3
+
5
c
4
(
1
)
(
i
)
4
−
i
5
=
2
−
10
+
5
−
10
+
5
=
−
8
.
© examsnet.com
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