# Python Language Arithmétique complexe avancée

## Exemple

Le module `cmath` inclut des fonctions supplémentaires pour utiliser des nombres complexes.

``````import cmath
``````

Ce module peut calculer la phase d'un nombre complexe, en radians:

``````z = 2+3j # A complex number
cmath.phase(z) # 0.982793723247329
``````

Il permet la conversion entre les représentations cartésiennes (rectangulaires) et polaires des nombres complexes:

``````cmath.polar(z) # (3.605551275463989, 0.982793723247329)
cmath.rect(2, cmath.pi/2) # (0+2j)
``````

Le module contient la version complexe de

• Fonctions exponentielles et logarithmiques (comme d'habitude `log` est le logarithme naturel et `log10` le logarithme décimal):

``````  cmath.exp(z) # (-7.315110094901103+1.0427436562359045j)
cmath.log(z) # (1.2824746787307684+0.982793723247329j)
cmath.log10(-100) # (2+1.3643763538418412j)
``````
• Racines carrées:

``````  cmath.sqrt(z) # (1.6741492280355401+0.8959774761298381j)
``````
• Fonctions trigonométriques et leurs inverses:

``````  cmath.sin(z)  # (9.15449914691143-4.168906959966565j)
cmath.cos(z)  # (-4.189625690968807-9.109227893755337j)
cmath.tan(z)  # (-0.003764025641504249+1.00323862735361j)
cmath.asin(z) # (0.5706527843210994+1.9833870299165355j)
cmath.acos(z) # (1.0001435424737972-1.9833870299165355j)
cmath.atan(z) # (1.4099210495965755+0.22907268296853878j)
cmath.sin(z)**2 + cmath.cos(z)**2 # (1+0j)
``````
• Fonctions hyperboliques et leurs inverses:

``````  cmath.sinh(z)  # (-3.59056458998578+0.5309210862485197j)
cmath.cosh(z)  # (-3.7245455049153224+0.5118225699873846j)
cmath.tanh(z)  # (0.965385879022133-0.009884375038322495j)
cmath.asinh(z) # (0.5706527843210994+1.9833870299165355j)
cmath.acosh(z) # (1.9833870299165355+1.0001435424737972j)
cmath.atanh(z) # (0.14694666622552977+1.3389725222944935j)
cmath.cosh(z)**2 - cmath.sin(z)**2  # (1+0j)
cmath.cosh((0+1j)*z) - cmath.cos(z) # 0j
``````