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NDA Math Complex Numbers
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© examsnet.com
Question : 16
Total: 66
What is the modulus of the complex number
i
2
n
+
1
(
−
i
)
2
n
−
1
, where
n
∈
N
and
i
=
√
−
1
?
[NDA-I 2021]
−
1
1
√
2
2
Validate
Solution:
👈: Video Solution
Concept
Iota power:
i
2
=
−
1
i
3
=
−
i
Calculation:
Given:
i
2
n
+
1
(
−
i
)
2
n
−
1
Put
n
=
1
(
n
∈
N
)
=
i
3
(
−
i
)
1
=
i
2
i
(
−
i
)
=
(
−
1
)
(
−
i
2
)
=
(
−
1
)
(
1
)
=
−
1
So, by putting any value of
n
we get the
−
1
Hence the modulus of the complex number
i
2
n
+
1
(
−
i
)
2
n
−
1
is
−
1
.
© examsnet.com
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