If |z1|=|z2|=|z3|=1 and z1, z2, z3 are represented by the vertices of an equilateral triangle then

Question

If |z1|=|z2|=|z3|=1 and z1, z2, z3 are represented by the vertices of an equilateral triangle then (A) z1+z2+z3=0 (B) z1 z2 z3=1 (C) z1+z2+z3=1 (D) z1 z2 z3=0

Tardigrade Admin · Accepted Answer

All the three vertices lies on circle |z|=1 so there centroid at O i.e. (z1+z2+z3/3)=0

Q. If $∣ z_{1} ∣ = ∣ z_{2} ∣ = ∣ z_{3} ∣ = 1$ and $z_{1}, z_{2}, z_{3}$ are represented by the vertices of an equilateral triangle then

$z_{1} + z_{2} + z_{3} = 0$

$z_{1} z_{2} z_{3} = 1$

$z_{1} + z_{2} + z_{3} = 1$

$z_{1} z_{2} z_{3} = 0$

All the three vertices lies on circle $∣ z ∣ = 1$
so there centroid at $O$ i.e.
$\frac{z _{1} + z _{2} + z _{3}}{3} = 0$

Q. If ∣z1​∣=∣z2​∣=∣z3​∣=1 and z1​,z2​,z3​ are represented by the vertices of an equilateral triangle then

z1​+z2​+z3​=0

z1​z2​z3​=1

z1​+z2​+z3​=1

z1​z2​z3​=0