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

If z = -5 + 3i , find the value of (z^(4)+9z^(3)+26z^(2)-14z + 8) .

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

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

If |z_(1)|=1,|z_(2)|=1,|(1)/(z_(1))+(1)/(z_(2))|=(3)/(2) then find the value of 2|z_(1)+z_(2)|]|=(3)/(2) then

If z_(1),z_(2),z_(3) are distinct nonzero complex numbers and a,b,c in R^(+) such that (a)/(|z_(1)-z_(2)|)=(b)/(|z_(2)-z_(3)|)=(c)/(|z_(3)-z_(1)|) Then find the value of (a^(2))/(z_(1)-z_(2))+(b^(2))/(z_(2)-z_(3))+(c^(2))/(z_(3)-z_(1))