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Let z 1 , z 2 and z 3 be three complex numbers on the circle |z| = 1 with arg (z 1 ) = 4 – π , arg(z 2 ) = 0 and arg(z 3 ) = 4 π . If 2 1 3 3 2 2 1 z z z z z z + + = α + β 2 , α, β ∈ Z, then the value of α 2 + β 2 is :

1. 24
2. 41
3. 31
4. 29

Correct answer: 29

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