mathscomplexe.py

Created by condouarthur

Created on April 21, 2023

782 Bytes


z=a+ib
conjuguée = a-ib
IzI = Sqrt(a2+b2)
IzI2=a2+b2
Inégalité triangulaire :
  Iz+wI<IzI + IwI
z = p(cos(T)+isin(T))
p=IzI 
T solution de cos(T)=Re(z/IzI) et sin(T)=Im(z/IzI)
exp(iT) =(cos(T)+isin(T)
soit z = pexp(iT)
cos(T)=eit + e-it / 2
sin(T)= eit - eit /2i
Formule de Moivre :
  (eit)^n = eitn
  soit (cos(t)+isin(t))^n= cos nt + isin nt 
Angle Moitié :
  1 + e^ia = 2cos(a/2)e^ia/2
  1 - e^ia = -2isin(a/2)e^ia/2
  e^ia +- e^ib = e^i(b+a/2)(e^-i(b-a)/2) +-e^i(b-a)/2)

Racine enième :
  ek = exp(2ipik/n)
calculer la racine carrée d'un nombre complexe : 
  z = a+id 
  On pose w = c+id tel que w2 = z = c2-d2 + 2icd
  puis reconnaitre
  Si trop compliqué on peut rajouter une troisième équation :
    IwI2 = IzI soit :
      c2+d2 = sqrt(a2+b2)

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