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

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)| = |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) and z_(2) be two complex numbers such that z_(1)+z_(2)=5 and z_(1)^(3)+z_(2)^(3)=20+15i Then, |z_(1)^(4)+z_(2)^(4)| equals -

Let z_1 and z_2 be two complex numbers satisfying |z_1|=9 and |z_2-3-4i|=4 Then the minimum value of |z_1-Z_2| is

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