If `|z^3+1/z^3|<=2` then `|z+1/z|` cannot exceed

If |z^(3)+(1)/(z^(3))|<=2 then |z+(1)/(z)| cannot exceed

If z^(2) + z + 1 = 0 , where z is a complex number , prove that ( z + 1/z)^(2) + ( z^(2) + 1/z^(2)) + (z^(3) + 1/z^(3))^(2) + (z^(4) + 1/z^(4))^(2) + (z^(5) + 1/z^(5)) ^(2) + ( z^(6) + 1/z^(6)) = 12 .

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

If x,y,z are different and Delta = {:|( x,x^(2) , 1+x^(3)),( y,y^(3) ,1+y^(3)),( z,z^(3) ,1+z^(3)) |:} then value of delta?

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^(2) + z + 1 = 0 where z is a complex num ber, then (z+(1)/(z))^(2)+(z^(2)+(1)/(z^(2)))^(2)+(z^(3)+(1)/(z^(3)))^(2) equal

If z_1, z_2, z_3 are the points A, B, C in the Argand Plane such that 1/(z_2-z_3)+1/(z_3-z_1)+1/(z_1-z_2)=0 , Prove that ABC is an equilateral triangle .

If z ^(2) + z + 1 = 0, where z is a complex number, then the value of (z + (1)/(z)) ^(2) + (z ^(2) + (1)/( z ^(2))) ^(2) + (z ^(3) + (1)/(z ^(3))) ^(2) +...( z ^(6) + (1)/(z ^(6)) )^(2) is

Suppose z satisfies the equation z^(2) + z + 1 = 0."Let" omega = (z+(1)/(z))^(2) + (z^(2) + (1)/(z^(2)))^(2) + (z^(3) + (1)/(z^(3)))+...+(z^(9) + (1)/(z^(9)))^(2) then |omega + sqrt(301) i| is equal to ____________