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 the square root of -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) / (c^2 + d^2) + (bc - ad)i / (c^2 + d^2) 

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

|a + bi| = sqrt(a^2 + b^2) 

Note: the above equations are for mathematical reference only, and should not be treated as something you can insert directly into code.

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().

Important Instructions:

• 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.
• 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 also allow you to compare a Complex number with objects of other types for equality and inequality, respectively.
• Provide a 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.

Use the following main function to test your code copy and paste after the code of the class.

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') if __name__ == "__main__": # execute only if run as a script main()

The function prompts the user to enter two Complex numbers. The input should be provided as two numbers separated by a space. The program displays the two complex numbers, their absolute values, the result of their addition, subtraction, multiplication, and division. It also displays the result of comparing the two Complex numbers using the different comparison operators.

The output from your program must be similar to and use the same format as the following sample output, where input from the user is shown in red:

>>> 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() Enter the first complex number: 3 4 Enter the second complex number: 2 -4 c1 is (3.0, 4.0i) c2 is (2.0, -4.0i) |(3.0, 4.0i)| = 5.0 |(2.0, -4.0i)| = 4.47213595499958 (3.0, 4.0i) + (2.0, -4.0i) = 5.0 (3.0, 4.0i) - (2.0, -4.0i) = (1.0, 8.0i) (3.0, 4.0i) * (2.0, -4.0i) = (22.0, -4.0i) (3.0, 4.0i) / (2.0, -4.0i) = (-0.5, 1.0i) Is c1 < c2? False Is c1 <= c2? False Is c1 > c2? True Is c1 >= c2? True Is c1 == c2? False Is c1 != c2? True Is c1 == 'Hello There'? False Is c1 != 'Hello There'? True >>> main() Enter the first complex number: 3.5 -2.5 Enter the second complex number: -3.5 2.5 c1 is (3.5, -2.5i) c2 is (-3.5, 2.5i) |(3.5, -2.5i)| = 4.301162633521313 |(-3.5, 2.5i)| = 4.301162633521313 (3.5, -2.5i) + (-3.5, 2.5i) = 0 (3.5, -2.5i) - (-3.5, 2.5i) = (7.0, -5.0i) (3.5, -2.5i) * (-3.5, 2.5i) = (-6.0, 17.5i) (3.5, -2.5i) / (-3.5, 2.5i) = -1.0 Is c1 < c2? False Is c1 <= c2? True Is c1 > c2? False Is c1 >= c2? True Is c1 == c2? True Is c1 != c2? False Is c1 == 'Hello There'? False Is c1 != 'Hello There'? True >>>