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Mathematics
Mathematics
Problem
If
a
=
cos
(
2
π
7
)
+
i
sin
(
2
π
7
)
a = \cos \left( \frac{2\pi}{7} \right) + i \sin \left( \frac{2\pi}{7} \right)
a
=
cos
(
7
2
π
)
+
i
sin
(
7
2
π
)
, where
i
=
−
1
i = \sqrt{-1}
i
=
−
1
, find the quadratic equation whose roots are
α
=
a
+
a
2
+
a
4
\alpha = a + a^2 + a^4
α
=
a
+
a
2
+
a
4
and
β
=
a
3
+
a
5
+
a
6
\beta = a^3 + a^5 + a^6
β
=
a
3
+
a
5
+
a
6
.
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