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Other
Quantitative Aptitude
HCF and LCM
What is the s...
Question
What is the smallest positive integer n for which
1
+
i
2
n
=
1
-
i
2
n
?
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Solution
1
+
i
2
n
=
1
-
i
2
n
⇒
1
+
i
2
n
=
1
-
i
2
n
⇒
1
2
+
i
2
+
2
i
n
=
1
2
+
i
2
-
2
i
n
⇒
1
-
1
+
2
i
n
=
1
-
1
-
2
i
n
[
∵
i
2
=
-
1
]
⇒
2
i
n
=
-
2
i
n
⇒
2
i
n
=
-
1
)
n
(
2
i
n
⇒
(
-
1
)
n
=
1
⇒
n
is
a
multiple
of
2
Thus, the smallest positive integer n for which
1
+
i
2
n
=
1
-
i
2
n
is 2.
Suggest Corrections
2
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