Ivan Shishkin, Rye (1878)

Problems/General algebraUnreviewed

Some irrational numbers

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This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

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Let P∈Q[X]P \in \mathbb{Q}[X] be an irreducibleFR polynomial of degree ⩾3\geqslant 3 having exactly two non-real roots, zz and its conjugate zˉ\bar{z}. Show that Im⁡(z)∉Q\operatorname{Im}(z) \notin \mathbb{Q}.

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