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Byju's Answer
Standard VIII
Mathematics
Cube-Root of a Negative Perfect Cube
Show that -√-...
Question
Show that
(
−
√
−
1
)
4
n
+
3
=
i
, where n is a positive integer.
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Solution
We have
(
−
√
−
1
)
4
n
+
3
=
(
−
i
)
4
n
+
3
[
∵
√
−
1
=
i
]
=
(
−
i
)
4
n
×
(
−
i
)
3
=
[
(
−
i
)
4
]
n
×
(
−
i
)
3
=
(
1
×
i
)
=
i
[
∵
(
−
i
)
4
=
1
and
−
i
3
=
−
(
−
i
)
=
i
]
Hence,
(
−
√
−
1
)
4
n
+
3
=
i
.
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18
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Cube-Root of a Negative Perfect Cube
Standard VIII Mathematics
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