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Mathematics
Problem
If
z
2
+
z
+
1
=
0
z^2 + z + 1 = 0
z
2
+
z
+
1
=
0
, where
z
z
z
is a complex number, the value of
(
z
+
1
z
)
2
+
(
z
2
+
1
z
2
)
2
+
(
z
3
+
1
z
3
)
2
+
⋯
+
(
z
6
+
1
z
6
)
2
\left(z + \frac{1}{z}\right)^2 + \left(z^2 + \frac{1}{z^2}\right)^2 + \left(z^3 + \frac{1}{z^3}\right)^2 + \dots + \left(z^6 + \frac{1}{z^6}\right)^2
(
z
+
z
1
)
2
+
(
z
2
+
z
2
1
)
2
+
(
z
3
+
z
3
1
)
2
+
⋯
+
(
z
6
+
z
6
1
)
2
is a. 18 b. 54 c. 6 d. 12
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