OK so I have a programming assignment and I need to create a class that represents Complex Numbers (good so far), add them to a list(good so far), and then output whether each individual number is real (a+0x), imaginary (0+bx), or complex (a+bx). A Complex object is made by initializing the real portion and imaginary portion     Complex(int _real, int _imag) { real = _real; imag = _imag; };    Complex(int _real) {real = _real; imag = 0;};    Complex() { real, imag = 0;}The problem is my professor has silly stipulations such as all of the data fields must be private and there can be no get methods to access any portion of an indivdual Complex number from outside the class.Instead the only public methods I have to work with are plus, subtract, and multiply methods that take another Complex number and return a sum, difference and product of the two respectively and a conjugate method that returns an individual Complex's conjugate. With only those four public methods at my disposal, what formula can I use to compute whether an individual number is real, imaginary or complex?This is less a coding issue and more of a logic issue I know.
Complex Number help
java;object oriented