Question

Python has the complex class for performing complex number arithmetic. For this assignment, you will design and implement your own Complex class. Note that the complex class in Python is named in lowercase, while our custom Complex class is named with C in uppercase.

A complex number is of the form a + bi, where a and b are real numbers and i is √-1. The numbers a and b are known as the real part and the imaginary part of the complex number, respectively.

You can perform addition, subtraction, multiplication, and division for complex numbers using the following formulas:

(a + bi) + (c + di) = (a + c) + (b + d)i

(a + bi) - (c + di) = (a - c) + (b - d)i

(a + bi) * (c + di) = (ac - bd) + (bc + ad)i

(a + bi) / (c + di) = (ac + bd)/(c2 + d2) + (bc - ad)i/(c2 + d2)

You can also obtain the absolute value (or length) of a complex number using the formula:

|a + bi| = _______ √ a2 + b2

Implement a class named Complex for representing complex numbers with methods _ _add_ _, _ _sub_ _, _ _mul_ _, _ _truediv_ _, and _ _abs_ _ for performing complex-number operations using +, -, *, /, and abs(). Note: In python 3, _ _truediv_ _ is used to override / and _ _floordiv_ _ is used to override //. The _ _abs_ _(self) special method is used to override the absolute value function; this will allow you to write abs(c), where c is an object of the class Complex. Also, implement the comparison methods _ _eq_ _, _ _ne_ _, _ _lt_ _, ...etc. to compare two Complex numbers based on their length. For the purpose of this assignment, assume that Complex numbers are compared based on the values of their lengths. So, for two Complex numbers c1 and c2, c1 is less than c2, if and only if abs(c1) < abs(c2). Similarly c1 equals c2 if and only if abs(c1) equals abs(c2). The methods _ _eq_ _ and _ _ne_ _ should allow you to compare a Complex number with objects of other types for equality and inequality, respectively.

This is the constructor __init__(self, a = 0, b = 0) to create a complex number a + bi with the default values 0 and 0 for a and b. Your _ _str_ _ method returns the Complex number as a string of the form (a, bi) (it should look as in the sample output below.) If b is 0, it simply returns a --without parentheses. Likewise if a is 0, it returns bi. If both a and b are 0, it returns the string 0. So, the parentheses will be part of the string representation only when both a and b are not 0.

The main function is provided and the code should go with it--copy and paste after the code of the class--

def main():

def main():
    input_line = input("Enter the first complex number: ")
    input_line = list(map(float,input_line.split()))
    a, b = input_line[0], input_line[1]
    c1 = Complex(a, b)
    input_line = input("Enter the second complex number: ")
    input_line = list(map(float,input_line.split()))
    a, b = input_line[0], input_line[1]
    c2 = Complex(a, b)
   
    print()
    print("c1 is", c1)
    print("c2 is", c2)
    print("|" + str(c1) + "| = " + str(abs(c1)))
    print("|" + str(c2) + "| = " + str(abs(c2)))
    
    print(c1, " + ", c2, " = ", c1 + c2)
    print(c1, " - ", c2, " = ", c1 - c2)
    print(c1, " * ", c2, " = ", c1 * c2)
    print(c1, " / ", c2, " = ", c1 / c2)
    
    print("Is c1 < c2?", c1 < c2)
    print("Is c1 <= c2?", c1 <= c2)
    print("Is c1 > c2?", c1 > c2)
    print("Is c1 >= c2?", c1 >= c2)
    print("Is c1 == c2?", c1 == c2)
    print("Is c1 != c2?", c1 != c2)
    print("Is c1 == 'Hello There'?", c1 == 'Hello There')
    print("Is c1 != 'Hello There'?", c1 != 'Hello There')
    
main()

Here is a example of what the output should look like

>>> main()
Enter the first complex number: 2.5 4.5
Enter the second complex number: -2.5 11.2

c1 is (2.5, 4.5i)
c2 is (-2.5, 11.2i)
|(2.5, 4.5i)| = 5.1478150704935
|(-2.5, 11.2i)| = 11.475626344561764
(2.5, 4.5i) + (-2.5, 11.2i) = 15.7i
(2.5, 4.5i) - (-2.5, 11.2i) = (5.0, -6.699999999999999i)
(2.5, 4.5i) * (-2.5, 11.2i) = (-56.65, 16.75i)
(2.5, 4.5i) / (-2.5, 11.2i) = (0.335257043055661, -0.2980484471106386i)
Is c1 < c2? True
Is c1 <= c2? True
Is c1 > c2? False
Is c1 >= c2? False
Is c1 == c2? False
Is c1 != c2? True
Is c1 == 'Hello There'? False
Is c1 != 'Hello There'? True
>>> main()

Here is what in have so far (just the class function but the main() function that is given should be there)

class Complex(object):
def __init__(self, a=0, b=0):
'''create a complex number a +bi with default values 0 and 0 for a and b'''
self._a = a
self._b = b

def __str__(self):

def __add__(self, other):
'''add method returns the sum of two complex numbers'''
  return (self._a + other._a) + (self._b + other._b)

def __sub__(self, other):
'''sub method subtracts two complex numbers'''

def __mul__(self, other):
'''mul method multiplies two compex numbers'''

def __truediv__(self, other):
'''truediv method devides two complex numbers'''
  
def __abs__(self):
'''abs method returns absolute value for two comlex numbers'''

def __eq__(self, other):

def __ne__(self, other):

def __lt__(self, other):

def __le__(self, other):

def __gt__(self, other):

def __ge__(self, other):
  

Answer 1

Screenshot:

CODE:

import math

class Complex(object):
    def __init__(self, a=0, b=0):
        '''create a complex number a +bi with default values 0 and 0 for a and b'''
        self._a = a
        self._b = b
      
    def __str__(self):
        if (self._a != 0) and (self._b != 0):
            return '('+str(self._a)+','+str(self._b)+ 'i)'
        elif self._a != 0:
            return str(self._a)
        elif self._b != 0:
            return str(self._b) + 'i'
      
    def __add__(self, other):
        '''add method returns the sum of two complex numbers'''
        return Complex(self._a + other._a,
                           self._b + other._b)
      
    def __sub__(self, other):
        '''sub method subtracts two complex numbers'''
        return Complex(self._a - other._a,
                           self._b - other._b)
      
    def __mul__(self, other):
        '''mul method multiplies two compex numbers'''
        return Complex(self._a*other._a - self._b*other._b,
                           self._b*other._a + self._a*other._b)
      
    def __truediv__(self, other):
        '''truediv method devides two complex numbers'''
        sr, si, ore, oi = self._a, self._b, other._a, other._b # short forms
        r = float(ore**2 + oi**2)
        return Complex((sr*ore+si*oi)/r, (si*ore-sr*oi)/r)
        
    def __abs__(self):
        '''abs method returns absolute value for two comlex numbers'''
        return math.sqrt(self._a**2 + self._b**2)
      
    def __eq__(self, other):
        if not isinstance(other, Complex):
            return NotImplemented
        return abs(self)==abs(other)
      
    def __ne__(self, other):
        if not isinstance(other, Complex):
            return NotImplemented
        return abs(self)!=abs(other)
      
    def __lt__(self, other):
        return abs(self)<abs(other)
      
    def __le__(self, other):
        return abs(self)<=abs(other)
      
    def __gt__(self, other):
        return abs(self)>abs(other)
      
    def __ge__(self, other):
        return abs(self)>=abs(other)
  
def main():
    input_line = input("Enter the first complex number: ")
    input_line = list(map(float,input_line.split()))
    a, b = input_line[0], input_line[1]
    c1 = Complex(a, b)
    input_line = input("Enter the second complex number: ")
    input_line = list(map(float,input_line.split()))
    a, b = input_line[0], input_line[1]
    c2 = Complex(a, b)
    print()
    print("c1 is", c1)
    print("c2 is", c2)
    print("|" + str(c1) + "| = " + str(abs(c1)))
    print("|" + str(c2) + "| = " + str(abs(c2)))
    print(c1, " + ", c2, " = ", c1 + c2)
    print(c1, " - ", c2, " = ", c1 - c2)
    print(c1, " * ", c2, " = ", c1 * c2)
    print(c1, " / ", c2, " = ", c1 / c2)
    print("Is c1 < c2?", c1 < c2)
    print("Is c1 <= c2?", c1 <= c2)
    print("Is c1 > c2?", c1 > c2)
    print("Is c1 >= c2?", c1 >= c2)
    print("Is c1 == c2?", c1 == c2)
    print("Is c1 != c2?", c1 != c2)
    print("Is c1 == 'Hello There'?", c1 == 'Hello There')
    print("Is c1 != 'Hello There'?", c1 != 'Hello There')