Let z₁ and z₂ be two non real complex cube roots of unity and ${|z - z_{1}|}^{2} + {|z - z_{2}|}^{2} = λ$ be the equation of a circle with z₁, z₂ as ends of a diameter, then the value of $λ$ is

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answer is 3.

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Detailed Solution

$| z - ω | + | z - ω |^{2} = λ$

$z_{1} = ω, z_{2} = ω^{2} \Rightarrow λ = {|(ω - ω^{2})|}^{2} = {|(\frac{- 1 + i \sqrt{3}}{2} - \frac{- 1 - i \sqrt{3}}{2})|}^{2} = {|(i \sqrt{3})|}^{2} = 3$

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