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MCQMediumJEE Main 2025 · 22 January, Shift 1Complex Numbers Basics

Mathematics Question from JEE Main 2025 · 22 January, Shift 1

Let z1,z2,z3z_1, z_2, z_3 be three complex numbers on the circle ∣z∣=1|z| = 1 with arg⁡(z1)=−π4,arg⁡(z2)=0\arg(z_1) = -\frac{\pi}{4}, \arg(z_2) = 0 and arg⁡(z3)=π4\arg(z_3) = \frac{\pi}{4}. If ∣z1z2‾+z2z3‾+z3z1‾∣2=α+β2|z_1 \overline{z_2} + z_2 \overline{z_3} + z_3 \overline{z_1}|^2 = \alpha + \beta \sqrt{2}, where α,β∈Z\alpha, \beta \in \mathbb{Z}, then the value of α2+β2\alpha^2 + \beta^2 is :

  • A

    2424

  • B

    4141

  • C

    3131

  • D

    2929

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