Final answer:
A Complex class in programming encapsulates operations with complex numbers, using constructors and member functions to manage arithmetic. Multiplying a complex number by its conjugate results in a real number, applicable in quantum mechanics when dealing with probabilities.
Step-by-step explanation:
The Complex class described in the question is designed to represent and perform arithmetic with complex numbers in a programming context. A complex number has a real part and an imaginary part, often expressed as a + bi, where a is the real part, b is the imaginary part, and i is the square root of -1. Utilizing double variables for the real and imaginary components, the Complex class encapsulates both parts as private data members and provides a constructor to initialize these values. The public member functions include an add function that combines the real parts and imaginary parts of two complex numbers.
To elaborate on complex arithmetic referenced in the question, when multiplying a complex number by its conjugate, such as (a + ib) * (a - ib), the result is a real number since the product will be a² + b². This property eliminates the complex parts and gives a real value. In quantum mechanics, where wave functions often involve complex numbers, probabilities of finding a particle are calculated using the modulus squared of these functions, which are also real-valued results due to the nature of complex conjugates.