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Complex roots of unity ordered pairs

1925SpecialistComplex NumbersNumber Theory

2022 AIME I · 2022

Let $w = \frac{\sqrt{3}+i}{2}$ and $z = \frac{-1+i\sqrt{3}}{2}$, where $i = \sqrt{-1}$. Find the number of ordered pairs $(r, s)$ of positive integers not exceeding $100$ that satisfy the equation $i \cdot w^r = z^s$.
0 students attempted0% solvedRating 1925

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