[" If "z_(1)z_(2),z_(3)" are soots of and "3z^(3)-1],[+a^(2)z+b=0" then find value of "],[(1)/(2-z_(2))+(1)/(z_(2)-z_(3))+(1)/(z_(3)-z_(1))=?]

If z_(1);z_(2) and z_(3) are the vertices of an equilateral triangle; then (1)/(z_(1)-z_(2))+(1)/(z_(2)-z_(3))+(1)/(z_(3)-z_(1))=0

If z_(1),z_(2),z_(3) are the vertices of an equilateral triangle,then value of (z_(2)-z_(3))^(2)+(z_(3)-z_(1))^(2)+(z_(1)-z_(2))^(2)

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))

If z_(1) + z_(2) + z_(3) = 0 and |z_(1)| = |z_(2)| = |z_(3)| = 1 , then value of z_(1)^(2) + z_(2)^(2) + z_(3)^(2) 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 find the value of |z_(1)+z_(2)+z_(3)|

If z_(1),z_(2) and z_(3) be unimodular complex numbers, then the maximum value of |z_(1)-z_(2)|^(2)+|z_(2)-z_(3)|^(2)+|z_(3)-z_(1)|^(2) , is

If z_(1),z_(2) and z_(3) be unimodular complex numbers, then the maximum value of |z_(1)-z_(2)|^(2)+|z_(2)-z_(3)|^(2)+|z_(3)-z_(1)|^(2) , is

If z_(0), z_(1),z_(2),...,z_(5) be 6^(th) roots of unity where z_(0)=1 then the value of (1)/(3)(2+z_(1))(2+z_(2))...(2+z_(5)) 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),.........Z_(n-1) are n^(th) roots of unity then the value of (1)/(3-Z_(1))+(1)/(3-Z_(2))+.........+(1)/(3-Z_(n-1)) is equal to