Re: HSC 2018 4U Marathon
(z-1)^6 +(z+1)^6 = 2z^6 + 30z^4 + 30z^2 +2 \\
z^6 + 15z^4 + 15z^2 + 2 = 0 = P(z)\\
\text{By inspection} z=\pm i \text{is a root, due to the coefficients being real the conjugate roots theorem applies} \\
\text{Performing Polynomial division of} \frac {P(z)}{z^2+1}...