Let `z_1z_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

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

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 , 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) = 0 and |z_(1)| = |z_(2)| = |z_(3)| = 1 , then value of z_(1)^(2) + z_(2)^(2) + z_(3)^(2) equals

Let z_(1),z_(2) be two complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| . Then,

Let z_(1) and z_(2) be two given complex numbers such that z_(1)/z_(2) + z_(2)/z_(1)=1 and |z_(1)| =3 , " then " |z_(1)-z_(2)|^(2) is equal to

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 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 :