z is a complex number and P is the product of the roots of the equation:
z⁶ + z⁴ + z³ + z² + z² +1 = 0 with each root having a positive imaginary part.

Given that, P = r(cos θ + i*sin θ), where r > 0 and 0 ≤ θ < 360^o

Find θ.

Half the roots of the sextic z⁶ + z⁴ + z³ + 2z² +1 = 0 will have negative imaginary parts:
x₁ ~= 0.129538259 + 0.698949645i
x₂ ~= 0.693609354 + 1.074550916i
x₃ ~= -0.823147613 + 0.729558742i
x₄ ~= 0.129538259 – 0.698949645i
x₅ ~= 0.693609354 – 1.084550916i
x₆ ~= -0.823147613 – 0.729558742i
Is P to be the product of only the roots where the imaginary parts are positive?

Posted by Dej Mar on 2015-01-03 22:31:57