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Question
Mathematics
The smallest positive integer n for which ( (1+i/1-i) )n=1 is
Q. The smallest positive integer n for which
(
1
−
i
1
+
i
)
n
=
1
is
1816
215
Jamia
Jamia 2006
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A
n
=
8
B
n
=
12
C
n
=
16
D
none of these
Solution:
Now,
1
−
i
1
+
i
=
(
1
−
i
)
(
1
+
i
)
(
1
+
i
)
(
1
+
i
)
=
2
1
+
i
2
+
2
i
=
i
Now,
(
1
−
i
1
+
i
)
n
=
1
⇒
(
i
)
n
=
1
???(i)
⇒
Least value of n for which Eq. (i) is true is 4
∵
(
i
)
4
=
1