An Easy Way And A Hard Way I

Algebra Level 5

j=0100x2j+1x2j \Large \left | \sum_{j=0}^{100} x^{2^j} + \dfrac1{x^{2^j}}\right |

Given that xx is a complex number satisfying the constraint x+1x=1 x + \dfrac1x = 1, find the value of the expression above.

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