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AIEEE 2006 Solved Paper
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© examsnet.com
Question : 111
Total: 143
If
z
2
+
z
+
1
=
0
, where
z
is complex number, then value of
(
z
+
1
z
)
2
+
(
z
2
+
1
z
2
)
2
+
(
z
3
+
1
z
3
)
2
+
.
.
.
.
.
.
.
.
.
.
.
.
+
(
z
6
+
1
z
6
)
2
is
18
54
6
12
Validate
Solution:
z
2
+
z
+
1
=
0
⇒
z
=
ω
or
ω
2
So,
z
+
1
z
=
ω
+
ω
2
=
−
1
z
2
+
1
z
2
=
ω
2
+
ω
=
−
1
z
3
+
1
z
3
=
ω
3
+
ω
3
=
2
z
4
+
1
z
4
=
−
1
z
5
+
1
z
5
=
−
1
and
z
6
+
1
z
6
=
2
∴
The given sum
=
1
+
1
+
4
+
1
+
1
+
4
=
12
© examsnet.com
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