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Algebra Level 4

(2ω+1ω)1000(ω21ω2)1000= ?\large { { \left (\frac { 2\omega +1 }{ \omega } \right ) }^{ 1000 }-{ \left (\frac { { \omega }^{ 2 }-1 }{ { \omega }^{ 2 } } \right ) }^{ 1000 } = \ ? }

Details and Assumptions

w w denote the cube root unity, which is the root of x3=1x^3 = 1 other than 11.

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