Lecture

Complex Numbers: Equations and Constructibility

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MATH-110(a): Advanced linear algebra I - vector spaces

L'objectif du cours est d'introduire les notions de base de l'algèbre linéaire (pour les futurs mathématiciens) et de démontrer rigoureusement les résultats principaux de ce sujet. ...

Description

This lecture covers the resolution of polynomial equations in the complex numbers field, including the fundamental theorem of algebra. It also explores the concept of constructibility with ruler and compass, discussing the Gauss-Wantzel theorem and the constructibility conditions for complex numbers. The lecture delves into the roots of unity, highlighting their properties and their relation to Fermat primes. Additionally, it explains the construction of points using ruler and compass, providing insights into the constructibility of complex numbers. The lecture concludes with a discussion on the constructibility of points and numbers in the complex plane.

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Related concepts (26)

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Fermat's Last Theorem

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Root of unity

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