(xvi)z^(2)+z+(1)/(4)

Factorize z^(2)+z+(1)/(4)

((3)/(7)z-(1)/(2))/(z-(1)/(4))-(3)/(14)=(1)/(7)

Solve : (z)/(2) - (z)/(3) - (z)/(4) = -1

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 the complex number A(z_(1)),B(z_(2)) and origin forms an isosceles triangle such that angle(AOB) = (2pi)/3 ,then (z_(1)^(2)+z_(2)^(2) +4z_(1)z_(2))/(z_(1)z_(2)) equals ________

If z=(i)/(2) then the value of the product (1+z)(1+z^(2))(1+z^(4))(1+z^(8)).........(1+z^(2n)) is equation

| ((1) / (2)) (z_ (1) + z_ (2)) + sqrt (z_ (1) z_ (2)) | + | ((1) / (2)) (z_ (1) + z_ (2)) - sqrt (z_ (1) z_ (2)) | = Choose the correct answer.1. | z_ (1) + z_ (2) |, 2. | z_ (1) | + | z_ (2) |, 3 | z_ (1) -z_ (2) |, 4. | Z_ (1) | - | z_ (2) |