Question 28
Determine the complex numbers $z$ și $w$ with the property that
$$
|z^{2n} + z^n w^n + w^{2n}| = 2^{2n} + 2^n + 1,
$$
for any positive integer $n$.
$$
|z^{2n} + z^n w^n + w^{2n}| = 2^{2n} + 2^n + 1,
$$
for any positive integer $n$.
MathNet 2025 — Part 02 (100 complete bilingual questions) Question 28
Math Olympiad Vault · MathNet 2025 — Part 02 (100 complete bilingual questions)