Let z 1, z 2 and z 3 be complex numbers such that | z 1|=| z 2|=| z 3|=| z 1+ z 2+ z 3|=2. If | z 1- z 2|= |z1-z3| and z2 ≠ z3. Then find the value of |z1+z2||z1+z3|.

Question

Let z 1, z 2 and z 3 be complex numbers such that | z 1|=| z 2|=| z 3|=| z 1+ z 2+ z 3|=2. If | z 1- z 2|= |z1-z3| and z2 ≠ z3. Then find the value of |z1+z2||z1+z3|. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

The triangle has cirumcentre at origin and its orthocentre lying on the circumcircle.

Q. Let z1​,z2​ and z3​ be complex numbers such that ∣z1​∣=∣z2​∣=∣z3​∣=∣z1​+z2​+z3​∣=2. If ∣z1​−z2​∣= ∣z1​−z3​∣ and z2​=z3​. Then find the value of ∣z1​+z2​∣∣z1​+z3​∣.

The triangle has cirumcentre at origin and its orthocentre lying on the circumcircle.

Q. Let $z_{1}, z_{2}$ and $z_{3}$ be complex numbers such that $∣ z_{1} ∣ = ∣ z_{2} ∣ = ∣ z_{3} ∣ = ∣ z_{1} + z_{2} + z_{3} ∣ = 2$ . If $∣ z_{1} - z_{2} ∣ =$ $∣ z_{1} - z_{3} ∣$ and $z_{2} \neq = z_{3}$ . Then find the value of $∣ z_{1} + z_{2} ∣ ∣ z_{1} + z_{3} ∣$ .