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NDA Math Complex Numbers
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© examsnet.com
Question : 53
Total: 66
What is
(
1
+
i
)
4
n
+
5
(
1
−
i
)
4
n
+
3
equal to,where n is a natural number and
i
=
√
−
1
?
[NDA II 2014]
2
2i
-2i
i
Validate
Solution:
(
1
+
i
)
4
n
+
5
(
1
−
i
)
4
n
+
3
=
(
1
+
i
)
4
n
+
3
×
(
1
+
i
)
2
(
1
−
i
)
4
n
+
3
=
(
1
+
i
1
−
i
×
1
+
i
1
+
i
)
4
n
+
3
×
(
1
+
i
)
2
=
(
1
+
i
2
+
2
i
1
−
i
2
)
4
n
+
3
×
(
1
+
i
)
2
=
(
2
i
2
)
4
n
+
3
=
i
4
n
+
3
(
1
+
i
2
+
2
i
)
=
−
i
(
2
i
)
=
2
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