Computer scienceProgramming languagesPythonObject-oriented programmingMethods

Math magic methods

Complex numbers 2.0

Report a typo

In this topic, we've defined the class ComplexNumber and several magic methods for this class. However, it makes sense to define a couple of other methods so that we can use this class to its full potential.

We need methods for subtraction and division.

Subtraction

If we have 2 complex numbers $x = a + bi$ and $y = c + di$ , then $x - y$ will equal $(a - c) + (b - d)i$ .

Division

For division, we need to calculate the reciprocal of a complex number. If $x = a + bi$ , then ${1 \over x} = {a \over a^2 + b^2} - {b \over a^2 + b^2}i$ .

${x \over y}$ can then be represented as $x * {1 \over y}$ .

Write a program in Python 3

class ComplexNumber:

def __init__(self, real_part, im_part):

self.real_part = real_part

self.im_part = im_part

def __add__(self, other):

real = self.real_part + other.real_part

imaginary = self.im_part + other.im_part

return ComplexNumber(real, imaginary)

def __mul__(self, other):

real = self.real_part * other.real_part - self.im_part * other.im_part

imaginary = self.real_part * other.im_part + other.real_part * self.im_part

return ComplexNumber(real, imaginary)

def __eq__(self, other):

return ((self.real_part == other.real_part) and

(self.im_part == other.im_part))

def __str__(self):

if self.im_part < 0:

sign = "-"

else:

sign = "+"

string = "{} {} {}i".format(self.real_part, sign, abs(self.im_part))

return string

# define the rest of the methods here

___

Create a free account to access the full topic