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|`.

Let z_(1), z_(2), z_(3) be three complex numbers such that |z_(1)| = |z_(2)| = |z_(3)| = 1 and z = (z_(1) + z_(2) + z_(3))((1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))) , then |z| cannot exceed

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 _______.

If z_1,z_2,z_3 are three complex numbers such that |z_1|=|z_2|=|z_3|=1 , find the maximum value of |z_1-z_2|^2+|z_2-z_3|^2+|z_3+z_1|^2

Let z_(1)z_(2),z_(3), be three complex number such that z_(1)+z_(2)+z_(3)=0 and |z_(1)|=|z_(2)|=|z_(3)|=1 then Let |z_(1)^(2)+2z_(2)^(2)+z_(3)^(2)| equals

If z_1,z_2,z_3 are complex number , such that |z_1|=2, |z_2|=3, |z_3|=4 , the maximum value |z_1-z_2|^(2) + |z_2-z_3|^2 + |z_3-z_1|^2 is :

Given the z_(1),z_(2) and z_(3) are complex numbers with |z_(1)|=1,|z_(2)|=1,|z_(3)|=1, and z_(1)+z_(2)+z_(3)=1 and z_(1)z_(2)z_(3)=1 find |(z_(1)+2)(z_(2)+2)(z_(3)+2)|

If z_(1),z_(2),z_(3) are three complex numbers, such that |z_(1)|=|z_(2)|=|z_(3)|=1 & z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=0 then |z_(1)^(3)+z_(2)^(3)+z_(3)^(3)| is equal to _______. (not equal to 1)

Let z_(1),z_(2),z_(3) be complex numbers (not all real) such that |z_(1)|=|z_(2)|=|z_(3)|=1 and 2(z_(1)+z_(2)+z_(3))-3z_(1)z_(2)z_(3) is real.Then,Max(arg(z_(1)),arg(z_(2)),arg(z_(3))) (Given that argument of z_(1),z_(2),z_(3) is possitive ) has minimum value as (k pi)/(6) where (k+2) is