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 the fourth roots of unity are z_(1), z_(2), z_(3), z_(4) then z_(1)^(2)+z_(2)^(2)+z_(3)^(2)+z_(4)^(2)=

If z^(1) =2 -I, z_(2)=1+i , find |(z_(1) + z_(2) + 1)/(z_(1)-z_(2) + 1)|

If |z^(2)-1|=|z|^(2)+1 , then z lies on :

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)| and arg (z_(1)//z_(2))=pi, then find z_(1)+z_(2) .

If z_(1)=sqrt(3)-i, z_(2)=1+i sqrt(3) , then amp (z_(1)+z_(2))=

If z_(1)=1+i, z_(2)=sqrt(3)+i, then arg ((z_(1))/(z_(2)))^(50)=

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)|=1 and z_(1)+z_(2)+z_(3)=0 , then z_(1),z_(2),z_(3) are vertices of

If |z_(1)+z_(2)|=|z_(1)-z_(2)| , then the difference of the arguments of z_(1) and z_(2) is