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.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84  import math as m
import cmath as c
class Complex:
"""
Author: César 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__":
r=90 OhmsL = 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(040j) # 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.
Lots of code for nothing. A common (the most common, as far as I know) way to write complex numbers in polar form is:
were mag is the magnitude, e is the Neperian constant, phase is the phase in radian. This writing is allowed in Python. See the following code:
The only lack in the native type is that you have to compute the phase by yourself. You may want to write a 1 line function for this, but certainly not a 50 lines class.