A Cube Root of Unity Power

★ 7/10complex numbers Substitution Casework

Problem

Two nonzero complex numbers $x, y$ satisfy $x^3 + y^3 = 0$ with $x \neq y$ . Find the value of

\left(\frac{x}{x-y}\right)^{2000} + \left(\frac{y}{y-x}\right)^{2000}.

Answer

Solution

Difficulty	7/10
Topics	complex numbers, Substitution, Casework

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