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Complex Numbers and Overload Operators

Certification: Advanced Level Accuracy: 100% Submissions: 2 Points: 15

Create a Python class called ComplexNumber that represents a complex number with real and imaginary parts. The class should overload arithmetic operators (+, -, *, /) to perform complex number operations and implement methods to calculate the magnitude (absolute value) and conjugate of the complex number. Additionally, implement appropriate string representation.

Example 1
    

  • Input: c1 = ComplexNumber(3, 4)
    • 

  • Output: 4 + 6i, 5.0
    • 

  • Explanation:
    
      
        
    • Step 1: Create a complex number (3 + 4i).
      • 
        
    • Step 2: Perform addition with another complex number.
      • 
        
    • Step 3: Calculate the magnitude √(3² + 4²) = 5.0.
      • 
    
    

    •
Example 2
    

  • Input: c1 = ComplexNumber(2, 3)
    • 

  • Output: -1 + 5i, 2 - 3i
    • 

  • Explanation:
    
      
        
    • Step 1: Perform complex number subtraction and multiplication.
      • 
        
    • Step 2: Return the result in standard a + bi format.
      • 
        
    • Step 3: Compute the conjugate of (2 + 3i), which is (2 - 3i).
      • 
    
    

    •
Constraints
    

  • Real and imaginary parts can be integers or floating-point numbers
    • 

  • Time Complexity: O(1) for all operations
    • 

  • Space Complexity: O(1) for all operations
    • 

  • Division by a complex number with both real and imaginary parts equal to zero should be handled gracefully
    •
Functions / MethodsObject-Oriented ProgrammingAmazonMicrosoft
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Hint
Solution

Solution Hints

    
        
  • Implement dunder methods for operator overloading: __add__, __sub__, __mul__, __truediv__
    • 
        
  • Use the formula for complex number multiplication: (a+bi)(c+di) = (ac-bd) + (ad+bc)i
    • 
        
  • Use the formula for complex number division: (a+bi)/(c+di) = ((ac+bd)/(c²+d²)) + ((bc-ad)/(c²+d²))i
    • 
        
  • Calculate magnitude using the Pythagorean theorem: |a+bi| = √(a² + b²)
    • 
        
  • The conjugate of a complex number a+bi is a-bi
    • 
        
  • Implement __str__ and __repr__ for string representation
    • 
        
  • Consider implementing comparison operators and other useful methods
    •

Steps to solve by this approach:

 Step 1: Create a class with real and imaginary attributes.

 Step 2: Implement __str__ method for string representation.

 Step 3: Overload arithmetic operators (+, -, *, /).

 Step 4: Overload comparison operator (==).

 Step 5: Test the implementation with various operations.

Submitted Code :