If `z^2+1/(z^2)=14 ,` find the value of `z^3+1/(z^3).`

If z_(1),z_(2)andz_(3) are complex numbers such that |z_(1)|=|z_(2)|=|z_(3)|=|z_(1)+z_(2)+z_(3)|=1 , find the value of |1/z_(1)+1/z_(2)+1/z_(3)| .

If z_1 = 3i and z_2 = -1 -i , find the value of arg z_1/z_2 .

If z_(1),z_(2),z_(3) are complex numbers such that |z_(1)|=|z_(2)|=|z_(3)|=1|(1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))|=1 Then find the value of |z_(1)+z_(2)+z_(3)| is :

If z=(1)/(2)(i sqrt(3)-1), then find the value of (z-z^(2)+2z^(3))(2-z+z^(2))

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 find the value of |z_(1)+z_(2)+z_(3)| is :

if z^2+z+1=0 , then the value of (z+1/z)^2+(z^2+1/z^2)^2+(z^3+1/z^3)^2+......+(z^21+1/z^21)^2 is

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 find the value of |z_(1)+z_(2)+z_(3)|

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 find the value of |z_(1) + z_(2) + z_(3)| .

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 find the value of |z_(1) + z_(2) + z_(3)| .

If z_1,z_2,z_3 are three complex numbers such that |z_1|=|z_2|=1 , find the maximum value of |z_1-z_2|^2+|z_2-z_3|^2+|z_3+z_1|^2