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Python offers a powerful data type for complex numbers in Cartesian form. Unfortunately, python does not offer support for complex numbers in polar form. This recipe contains a class that supports complex numbers in both Cartesian and polar form, and allows for arithmetic that mixes both forms.

Python, 88 lines
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import math as m
import cmath as c

class Complex:
    """
      Author: C├ęsar Otero
      Description: A complex number class which can do complex arithmetic
                   in both Cartesian and polar coordinates, or a mix of the two
    """
  
    def __init__(self, num=0, phase=0):
        if type(num) == complex:
            # cnum is in Cartesian form
            self.cnum      = num
            self.magnitude = abs(num)
            phaseRad = m.atan2(num.imag, num.real)
            self.phase     = m.degrees(phaseRad)
            
        else:
            # cnum is in polar form
            self.cnum      = m.cos(phase) + complex(0,m.sin(phase))
            self.magnitude = num
            self.phase     = phase

    def __str__(self):
        return str(self.magnitude) + " /_ (" + str(self.phase) + ") deg"

    def __add__(self,n):
        if type(n) == int:
            re = self.cnum.real + n
            im = self.cnum.imag
        elif type(n) == float:
            re = self.cnum.real + n
            im = self.cnum.imag
        else:
            re = self.cnum.real + n.cnum.real
            im = self.cnum.imag + n.cnum.imag
            
        z = re+complex(0,im)
        return Complex(z)
    
    def __radd__(self,n):
        if type(n) == int:
            re = self.cnum.real + n
            im = self.cnum.imag
        elif type(n) == float:
            re = self.cnum.real + n
            im = self.cnum.imag
        else:
            re = self.cnum.real + n.cnum.real
            im = self.cnum.imag + n.cnum.imag
            
        z = re+complex(0,im)
        return Complex(z)

    def __div__(self,n):
        magnitude = self.magnitude / n.magnitude
        phase = self.phase - n.phase
        return Complex(magnitude, phase)

    def __rdiv__(self,n):
        magnitude = n.magnitude / self.magnitude
        phase = n.phase - self.phase 
        return Complex(magnitude, phase)

if __name__=="__main__":
    """
      Example application of the Complex class, using both Cartesian and polar forms.
      In this example, we have a simple model for a RLC AC circuit

        |---r=90 Ohms----L=160j Ohms -----|        
        |                                 |
      pSource=750 /_ 30 deg          C = -40j Ohms          
        |                                 |                                                  
        |---------------------------------|
    """              
    
    pSource = Complex(750,30) # power source, in polar form 
                              # with a magnitude of 750 volts, and angle of 30 
                              # degrees.
    r = 90                    # Ohms ( real part only )
    L = Complex(0+160j)       # Ohms ( Cartesian form )
    C = Complex(0-40j)        # Ohms ( Cartesian form )
    Z = r+L+C                 # total impedance    
    print "Impedance is ", Z
    
    I = pSource / Z
    print "Phase current is ", I
    

In some engineering and scientific applications it is useful to represent complex numbers in polar form, or mix polar form complex numbers with Cartesian form without having to worry about the details of converting from one type to the other before doing any arithmetic. This ability is inherit in other languages such as Matlab or IDL. This recipe is useful for extending python to be able to handle these types of calculations.

A better implementation could be achieved by inheriting directly from the python complex type.