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NDA Math Complex Numbers
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© examsnet.com
Question : 19
Total: 66
If
x
=
1
+
i
, then what is the value of
x
6
+
x
4
+
x
2
+
1
?
[NDA II 2019]
6
i
–
3
–
6
i
+
3
–
6
i
–
3
6
i
+
3
Validate
Solution:
Given,
x
=
(
1
+
i
)
then,
x
2
=
(
1
+
i
)
2
=
1
+
i
2
+
2
i
=
1
−
1
+
2
i
=
2
i
,
x
4
=
(
1
+
i
)
4
=
(
2
i
)
2
=
4
i
2
=
4
×
−
1
=
−
4
and
x
6
=
x
4
×
x
2
=
−
4
(
2
i
)
=
−
8
i
∴
x
6
+
x
4
+
x
2
+
1
=
−
8
i
+
(
−
4
)
+
2
i
+
1
=
−
6
i
−
3
© examsnet.com
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