If the complex numbers z1, z2 and z3 represent the vertices of an equilateral triangle such that |z1|=|z2|=|z3|, then

Question

If the complex numbers z1, z2 and z3 represent the vertices of an equilateral triangle such that |z1|=|z2|=|z3|, then (A) z1+z2+z3=0 (B) z1+z2-z3=0 (C) z1-z2+z3=0 (D) z1+z2+z3 ≠ 0

Tardigrade Admin · Accepted Answer

Let |z1|=|z2|=|z3|=k (say), ⇒ z1, z2, z3 lie on a circle with centre at the origin and radius k. As z1, z2, z3 are vertices of an equilateral triangle, the circumcentre and the centroid of the triangle coincide. Therefore, (1/3)(z1+z2+z3)=0 ⇒ z1+z2+z3=0

Q. If the complex numbers $z_{1}, z_{2}$ and $z_{3}$ represent the vertices of an equilateral triangle such that $∣ z_{1} ∣ = ∣ z_{2} ∣ = ∣ z_{3} ∣$ , then

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

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

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

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

Q. If the complex numbers z1​,z2​ and z3​ represent the vertices of an equilateral triangle such that ∣z1​∣=∣z2​∣=∣z3​∣, then

z1​+z2​+z3​=0

z1​+z2​−z3​=0

z1​−z2​+z3​=0

z1​+z2​+z3​=0

Q. If the complex numbers $z_{1}, z_{2}$ and $z_{3}$ represent the vertices of an equilateral triangle such that $∣ z_{1} ∣ = ∣ z_{2} ∣ = ∣ z_{3} ∣$ , then

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

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

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

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