∣z∣=1arg(z1)=−4π,arg(z2)=0,arg(z3)=4πz1=∣1∣e−4π=21−2iz2=1+0iz3=21+2iz1zˉ2=21−iz2zˉ3=21−iz3zˉ1=2(1+i)2z1zˉ2+z2zˉ3+z3zˉ1=2+i(1−2)∣z1zˉ2+z2zˉ3+z3zˉ1∣2=5−22α=5,β=−2α2+β2=29
Let z1,z2 and z3 be three complex numbers on the circle ∣z∣=1 with arg(z1)=4−π,arg(z2)=0 and arg(z3)=4π. If ∣z1zˉ2+z2zˉ3+z3zˉ1∣2=α+β2,α,β∈Z, then the value of α2+β2 is :
Held on 22 Jan 2025 · Verified 6 Jul 2026.
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