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|le,|z_(2) -2| le2,|z_(3) - 3|le 3, then find the greatest value of |z_(1) + z_(2) + z_(3)|

If |z_(1)|=2,|z_(2)|=3,|z_(3)|=4and|z_(1)+z_(2)+z_(3)|=5. "then"|4z_(2)z_(3)+9z_(3)z_(1)+16z_(1)z_(2)| is

If |z_(1)|=|z_(2)|andamp(z_(1))+amp(z_(2))=0, then

If |z|ge3, then determine the least value of |z+(1)/(z)| .

If |z_(1)| = |z_(2)| = ….. |z_(n)| = 1 , prove that |z_(1) + z_(2) + …….. z_(n)| = |(1)/(z_(1)) + (1)/(z_(2)) + ……….. + (1)/(z_(n))| .

If x_(1) = 3y_(1) + 2y_(2) -y_(3), " " y_(1)=z_(1) - z_(2) + z_(3) x_(2) = -y_(1) + 4y_(2) + 5y_(3), y_(2)= z_(2) + 3z_(3) x_( 3)= y_(1) -y_(2) + 3y_(3)," " y_(3) = 2z_(1) + z_(2) espress x_(1), x_(2), x_(3) in terms of z_(1) ,z_(2),z_(3) .

If |z_(1)|=|z_(2)| and arg (z_(1)//z_(2))=pi, then z 1 ​ +z 2 ​ is equal to

If arg (z^(1//2))=(1)/(2)arg(z^(2)+barzz^(1//3)), find the value of |z|.

If z_(1),z_(2)inC,z_(1)^(2)+z_(2)^(2)inR,z_(1)(z_(1)^(2)-3z_(2)^(2))=2 and z_(2)(3z_(1)^(2)-z_(2)^(2))=11, the value of z_(1)^(2)+z_(2)^(2) is

If z_(1),z_(2) and z_(3), z_(4) are two pairs of conjugate complex numbers, the find the value of arg(z_(1)/z_(4)) + arg(z_(2)//z_(3)) .