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NDA Math Complex Numbers
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© examsnet.com
Question : 11
Total: 66
If
i
=
√
−
1
, then how many values does
i
−
2
n
have for different
n
∈
ℤ
?
[NDA-II 2021]
One
Two
Four
Infinite
Validate
Solution:
👈: Video Solution
Given that,
i
=
√
−
1
To find
(
i
)
−
2
n
Let
i
=
r
(
cos
θ
+
i
sin
θ
)
⇒
r
=
1
,
θ
=
π
2
∴
i
=
(
cos
π
2
+
i
sin
π
2
)
∴
(
i
)
−
2
n
=
(
cos
π
2
+
i
sin
π
2
)
−
2
n
=
cos
(
−
2
n
π
2
)
+
i
sin
(
−
2
n
π
2
)
=
cos
(
n
π
)
−
i
sin
(
n
π
)
=
(
−
1
)
n
=
{
−
1
if n is odd
1
if
n
is even
© examsnet.com
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