The value of (-1+i root3)^1008+(-1-i root3)^1008

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∣ ∣ ∣ ∣ \begin{matrix} 1 + i & 1 - i & i 1 + i & i & 1 + i i & 1 + i & 1 - i \end{matrix} ∣ ∣ ∣ ∣

1 + (1 + i) + (1 + i)^{2} + (1 + i)^{3} =

(1 + i) (1 + i^{2}) (1 + i^{3}) (1 + i^{4})

{(\frac{1 + i \sqrt{3}}{1 - i \sqrt{3}})}^{6} + {(\frac{1 - i \sqrt{3}}{1 + i \sqrt{3}})}^{6}

(1 + i) (1 + i^{2}) (1 + i^{3}) (1 + i^{4})

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