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NDA Math Complex Numbers
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© examsnet.com
Question : 8
Total: 66
What is
8
n
+
7
∑
n
=
1
i
n
equal to, where
i
=
√
−
1
?
[NDA-II 2021]
−
1
1
i
−
i
Validate
Solution:
👈: Video Solution
Let
S
=
8
n
+
7
∑
n
=
1
i
n
S
=
i
+
i
2
+
i
3
+
.
.
.
+
i
8
n
+
7
=
i
[
(
i
)
8
n
+
7
−
1
i
−
1
]
=
i
[
i
4
(
2
n
+
1
)
+
3
−
1
i
−
1
]
=
i
(
i
3
−
1
i
−
1
)
[
∵
i
4
n
+
r
=
i
r
]
=
i
[
−
i
−
1
i
−
1
]
=
−
i
2
−
i
i
−
1
=
1
−
i
i
−
1
=
−
1
© examsnet.com
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