polyn.py

Created on May 22, 2025

434 Bytes

Nombre complexe a appelé une 
racine du polynome P si P(a)=0

FACTORISATION 
z^4 - a^4 = (z-a)(z^3 + az^2 +
a^2z + a^3)

Nombre a est racine ssi P peut se
factoriser par z-a

THEOREME
Un polynome non nul de degré n
admet au plus n racines dans C

DEFINITION 
On appelle racine n-ième de 
l'unité un nombre complexe tq
z^n = 1

CAS GENERAL 
L'ensemble des racines n-ièmes 
de l'unité est {e^(2ikpi)/n}
k e [|0; n-1|]

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polyn.py