Complex Numbers on Unit Circle (Jee Mains)

Algebra and Representation of Complex Numbers

Medium

Complex Numbers on Unit Circle

Let z₁, z₂ and z₃ be three complex numbers on the circle |z| = 1 with $\arg ({z_1}) = \frac{{ - \pi }}{4}$ , arg(z₂) = 0 and $\arg ({z_3}) = \frac{\pi }{4}$ .
If ${\left| {{z_1}{{\bar z}_2} + {z_2}{{\bar z}_3} + {z_3}{{\bar z}_1}} \right|^2} = \alpha + \beta \sqrt 2$ , α, β ∈ Z, then the value of α² + β² is :

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