Let `z_r(1 leq r leq 4)` be complex numbers such that `|z_r|=sqrt(r+1) and |30 z_1 + 20 Z_2 + 15 z_3+ 12 z_4 = k|z_1 z_2 z_3+z_2 z_3 z_4+z_3 z_4 z_1+z_4 z_1 z_2|`.Then the value of k equals

Let z_(r)(1<=r<=4) be complex numbers such that |z_(r)|=sqrt(r+1) and |30z_(1)+20Z_(2)+15z_(3)+12z_(4)=k|z_(1)z_(2)z_(3)+z_(2)z_(3)z_(4)+z_(3)z_(4)z_(1)+z_(4)z_(1)z_(2). Then the value of k equals

Let z_(r)(1<=r<=4) be complex numbers such that }z_(r)|=sqrt(r+1) and |30z_(1)+20z_(2)+15z_(3)+12z_(4)|=k|z_(1)z_(2)z_(3)+z_(2)z_(3)z_(4)+z_(3)z_(4)z_(1)+z_(4)z_(1)z_(2) then the value of k equals

If |z_1|=1, |z_2| = 2, |z_3|=3 and |9z_1 z_2 + 4z_1 z_3+ z_2 z_3|=12 , then the value of |z_1 + z_2+ z_3| is equal to

Let z_(1),z_(2) and z_(3) be complex numbers such that |z_(1)|=|z_(2)|=|z_(3)|=1 then prove that |z_(1)+z_(2)+z_(3)|=|z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1)|

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 :

If z_1,z_2, z_3 are complex numbers such that |z_1|=|z_2|=|z_3|=|1/z_1+1/z_2+1/z_3|=1 then |z_1+z_2+z_3| is equal to

If z_1,z_2, z_3 are complex numbers such that |z_1|=|z_2|=|z_3|=|1/z_1+1/z_2+1/z_3|=1 then |z_1+z_2+z_3| is equal to

If z_1,z_2, z_3 are complex numbers such that |z_1|=|z_2|=|z_3|=|1/z_1+1/z_2+1/z_3|=1 then |z_1+z_2+z_3| is equal to

If z_1,z_2, z_3 are complex numbers such that |z_1|=|z_2|=|z_3|=|1/z_1+1/z_2+1/z_3|=1 then |z_1+z_2+z_3| is equal to

If z_1 = 4 - 7i , z_2 = 2 + 3i and z_3 = 1 + i show that z_1 + (z_2 + z_3) = (z_1 + z_2)+z_3