Let z_1, z_2 and z_3 be three complex numbers on the circle |z|=1 with \arg (z_1) =\frac{-\pi}{4}, \arg (z_2) =0 and \arg (z_3) =\frac{\pi}{4}. If {|z_1 \overline{z}_2+z_2 \overline{z}_3+z_3 \overline{z}_1 |}^2 = \alpha+\beta \sqrt{2}, \alpha, \beta \in Z, then the value of \alpha^2+\beta^2 is: [22 Jan 2025 Shift 1]

Complex Numbers Part 2

Section: Mathematics

Question : 20 of 97

Marks: +1, -0

Let z1,z2 and z3 be three complex numbers on the circle |z|=1 with arg(z1)=‌

−π

,arg(z2)=0 and arg(z3)=‌

. If |z1z2+z2z3+z3z1|2‌‌= α+β√2,α,β∈Z, then the value of α2+β2 is:

[22 Jan 2025 Shift 1]

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