Let `z_r( 1le r le 4) ` be complex numbers such that `}z_r|=sqrt(r+1)` and `|30z_1+20z_2+15z_3+12z_4|=k|z_1z_2z_3+z_2z_3z_4+z_3z_4z_1+z_4z_1z_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)|

Let |z_1|=i,i=1,2,3,4and |16 z_1z_2z_3+9z_1z_2z_4+4z_1z_3z_4+z_2z_3z_4|=48 ,then the value of |1/barz_1+4/bar z_2+9/vec z_3+16/bar z_4|

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 :

a. Let z_(1),z_(2) and z_(3) be complex numbers such that |z_(1)|=|z_(2)|=|z_(3)|=rgt0 and z_(1)+z_(2)+z_(3)!=0 . Prove that |(z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1))/(z_(1)+z_(2)+z_(3))|=r b. Find all cube roots of sqrt(3)+i .

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