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NDA Math Complex Numbers
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© examsnet.com
Question : 20
Total: 66
What is the value of
[
i
+
√
3
2
]
2019
+
[
i
−
√
3
2
]
2019
?
[NDA II 2019]
1
–1
2i
–2i
Validate
Solution:
[
i
+
√
3
2
]
2019
+
[
i
−
√
3
2
]
2019
=
[
(
i
+
√
3
2
)
3
]
673
+
[
(
i
−
√
3
2
)
3
]
673
=
[
i
3
+
3
⋅
i
2
⋅
√
3
+
3
⋅
i
⋅
(
√
3
)
2
+
3
√
3
8
]
673
+
[
i
3
−
3
⋅
i
2
⋅
√
3
+
3
⋅
i
⋅
√
3
2
−
3
√
3
8
]
673
=
[
−
i
−
3
√
3
+
9
i
+
3
√
3
8
]
673
+
[
−
i
+
3
√
3
+
9
i
−
3
√
3
8
]
673
=
[
8
i
8
]
673
+
[
8
i
8
]
673
[
i
2
=
−
1
,
i
3
=
−
i
=
i
4
=
1
]
=
[
i
]
673
+
[
i
]
673
=
2
[
i
]
673
=
2
[
i
4
]
168
×
i
=
2
[
1
]
168
×
i
=
2
×
i
=
2
i
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