∣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 z_1, z_2 and z_3 be three complex numbers on the circle |z|=1 with arg (z_1 )= -π 4, arg (z_2 )=0 and arg (z_3 )= π 4. If |z_1 z_2+z_2 z_3+z_3…
JEE Main 2025 — Mathematics Algebra
2025mcqmedium
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 :
Official previous-year question
Held on 22 Jan 2025 · Verified 6 Jul 2026.
Options
- A
24
- B
29
- C
41
- D
31
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