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China Team Selection Test
2016 China Team Selection Test
2
China Team Selection Test 2016 TST 1 Day 1 Q2
China Team Selection Test 2016 TST 1 Day 1 Q2
Source: China Changsha
March 15, 2016
inequalities
complex numbers
China TST
Problem Statement
Find the smallest positive number
λ
\lambda
λ
, such that for any complex numbers
z
1
,
z
2
,
z
3
∈
{
z
∈
C
∣
∣
z
∣
<
1
}
{z_1},{z_2},{z_3}\in\{z\in C\big| |z|<1\}
z
1
,
z
2
,
z
3
∈
{
z
∈
C
∣
z
∣
<
1
}
,if
z
1
+
z
2
+
z
3
=
0
z_1+z_2+z_3=0
z
1
+
z
2
+
z
3
=
0
, then
∣
z
1
z
2
+
z
2
z
3
+
z
3
z
1
∣
2
+
∣
z
1
z
2
z
3
∣
2
<
λ
.
\left|z_1z_2 +z_2z_3+z_3z_1\right|^2+\left|z_1z_2z_3\right|^2 <\lambda .
∣
z
1
z
2
+
z
2
z
3
+
z
3
z
1
∣
2
+
∣
z
1
z
2
z
3
∣
2
<
λ
.
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