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Mathematics
Mathematics
Problem
Let
z
1
,
z
2
,
z
3
∈
C
z_1, z_2, z_3 \in \mathbb{C}
z
1
,
z
2
,
z
3
∈
C
such that
∣
z
1
∣
=
1
|z_1| = 1
∣
z
1
∣
=
1
,
∣
z
2
−
(
1
+
3
i
)
∣
=
3
|z_2 - (1 + \sqrt{3}i)| = 3
∣
z
2
−
(
1
+
3
i
)
∣
=
3
and
∣
z
3
−
3
−
3
3
i
∣
=
7
|z_3 - 3 - 3\sqrt{3}i| = 7
∣
z
3
−
3
−
3
3
i
∣
=
7
. If
∣
3
z
1
−
2
z
2
−
4
z
3
∣
|3z_1 - 2z_2 - 4z_3|
∣3
z
1
−
2
z
2
−
4
z
3
∣
is maximum then the value of
∣
z
3
−
z
1
∣
+
z
3
+
3
z
1
z
2
|z_3 - z_1| + \frac{z_3 + 3z_1}{z_2}
∣
z
3
−
z
1
∣
+
z
2
z
3
+
3
z
1
is equal to
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