Fifth Powers from a Quadratic

★ 5/10complex numbers Recursion algebra Vieta's Formulas

Problem

Complex numbers $z, w$ satisfy $z + w = 1$ and $zw = \mathrm{i}$ , where $\mathrm{i}$ is the imaginary unit. Find $z^5 + w^5$ .

Answer

Solution

Difficulty	5/10
Topics	complex numbers, Recursion, algebra, Vieta's Formulas

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