Final answer:
The subtraction of complex numbers (a, b) and (c, d) results in (a - c, b - d). Without the complete set of real and imaginary parts, the operation can't be performed. Division is more complex, involving the conjugate of the denominator.
Step-by-step explanation:
Overloading Subtraction and Division Operators in the ComplexType Class
When extending the definition of the class "ComplexType", to perform subtraction of complex numbers (a, b) and (c, d), the result is as follows: (a, b) - (c, d) leads to a new complex number where the real parts and the imaginary parts are subtracted respectively. Therefore, the correct answer is (a - c, b - d). For example, if a = 3, b = 13, and we subtract another complex number where c = -10 and d is not given, we wouldn't be able to perform the subtraction without the value of d.
Division in complex numbers is slightly more intricate. This operation involves multiplying the numerator and denominator by the conjugate of the denominator and simplifying. The formulaic approach for performing division is (ac + bd) / (c^2 + d^2) for the real part and (bc - ad) / (c^2 + d^2) for the imaginary part.
Subtracting and dividing complex numbers are analogous to vector subtraction and division in many ways. In vector operations, the subtraction is performed by flipping the vector to its negative and then adding it to the original vector, as suggested in the provided reference materials. While division is not commonly defined for vectors, the process for complex numbers can be compared to multiplying a vector by a scalar and involves finding a resultant quantity that considers both magnitude and direction.