Let `z_1, z_2,z_3` be three distinct complex numbers satisfying `|z_1- 1|=|z_2 - 1|= |z_3-1|`.If `z_1+z_2+z_3=3` then `z_1,z_2,z_3` must represent the vertices of

Let z_1, z_2, z_3 be three distinct complex numbers satisfying |z_1 - 1| = |z_2-1| = |z_3-1| . Let A , B, and C be the points represented in the Argand plane corresponding to z_1 , z_2 and z_3 respectively. Prove that z_1 + z_2 + z_3=3 if and only if Delta ABC is an equilateral triangle.

Let z_(1),z_(2),z_(3),z_(4) are distinct complex numbers satisfying |z|=1 and 4z_(3) = 3(z_(1) + z_(2)) , then |z_(1) - z_(2)| is equal to

Let z_1,z_2,z_3 be three complex numbers such that |z_1|=1,|z_2|=2,|z_3|=3 and |z_1+z_2+z_3|=1. Find |9z_1z_2+4z_1z_3+z_2z_3| .

If |z_(1)|=|z_(2)|=|z_(3)| and z_(1)+z_(2)+z_(3)=0 , then z_(1),z_(2),z_(3) are vertices of

Let z_1 and z_2 be two complex numbers satisfying |z_1|=9 and |z_2-3-4i|=4 Then the minimum value of |z_1-Z_2| is

If 2z_(1)-3z_(2)+z_(3)=0, then z_(1),z_(2) and z_(3) are represented by

Let z_1 , z _2 and z_3 be three complex numbers such that z_1 + z_2+ z_3 = z_1z_2 + z_2z_3 + z_1 z_3 = z_1 z_2z_3 = 1 . Then the area of triangle formed by points A(z_1 ), B(z_2) and C(z_3) in complex plane is _______.