Is λ \lambda a complex number?

Algebra Level 5

Find the smallest positive number λ \lambda , 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 \mathbb C \big| |z| < 1\} , if 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 .


The answer is 1.

Priyanshu Mishra by Priyanshu Mishra , 20, India

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1 solution

Zerocool 141
Nov 5, 2016

take 1 ,w,w^2 symmetrical here

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