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`

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 :

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) 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)

If z_(1),z_(2) and z_(3) be unimodular complex numbers, then the maximum value of |z_(1)-z_(2)|^(2)+|z_(2)-z_(3)|^(2)+|z_(3)-z_(1)|^(2) , is

If z_1,z_2,z_3 are three points lying on the circle |z|=2 then the minimum value of the expression |z_1+z_2|^2+|z_2+z_3|^2+|z_3+z_1|^2=

If z, z _1 and z_2 are complex numbers such that z = z _1 z_2 and |barz_2 - z_1| le 1 , then maximum value of |z| - Re(z) is _____.

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