Overloading Multiplication Operator - c++

Question

I am working on an assignment for my c++ class. We are having to overload several operators such as +, -, !=, =, etc. Well, I have all of them figured out except the multiplication. Everything I have tried gives an overflow or just doesn't compile. Not sure what I need for it.
Here is the header file that holds my overloads.
#ifndef COMPLEXNUMBER_H
#define COMPLEXNUMBER_H
#include<iostream>
using namespace std;
class ComplexNumber{
public:
double real, imaginary;
ComplexNumber(){
real = 0;
imaginary = 0;
}
ComplexNumber(double a, double b){
real = a;
imaginary = b;
}
ComplexNumber(double a){
real = a;
imaginary = 0;
}
ComplexNumber & operator= (const ComplexNumber & rhs){
if(this == &rhs){
return *this;
}
else{
real = rhs.imaginary;
imaginary = rhs.imaginary;
}
return *this;
}
ComplexNumber & operator+= (const ComplexNumber &rhs){
real += rhs.real;
imaginary += rhs.imaginary;
return *this;
}
ComplexNumber & operator-= (const ComplexNumber &rhs){
real -= rhs.real;
imaginary -= rhs.imaginary;
return *this;
}
const ComplexNumber operator+ (const ComplexNumber &rhs){
ComplexNumber result = *this;
result += rhs;
return result;
}
const ComplexNumber operator- (const ComplexNumber &rhs){
ComplexNumber result = *this;
result -= rhs;
return result;
}
const ComplexNumber operator* (const ComplexNumber &rhs){
return *this * rhs;
}
friend ostream & operator<< (ostream &out, const ComplexNumber &c){
out << "(" << c.real << (c.imaginary<0?" - ":" + ") << abs(c.imaginary) << " i)";
return out;
}
friend istream & operator>> (istream & in, ComplexNumber &c){
in >> c.real >> c.imaginary;
return in;
}
operator double(){
return real;
}
bool operator== (const ComplexNumber & rhs) const {
bool result = (this->real == rhs.real) && (this->imaginary == rhs.imaginary);
return result;
}
bool operator!= (const ComplexNumber &rhs) const{
return !(*this == rhs);
}
};
#endif
I know that multiplication operator is way off, but its just what I have at the moment. Here it is on its own. Any ideas would be greatly appreciated!!
const ComplexNumber operator* (const ComplexNumber &rhs){
return *this * rhs;
}

Answer 1

It gives you an overflow because of the way you call it. With your call, you are multiplying a complex number with a complex number, and it just keeps calling the same operator without doing anything. You could try to use some basic math and derive the formula for complex number multiplication. Specifically, let's say we have two complex numbers Z1 and Z2. Let Z1 = a + bi, where a is the real part, and b is the imaginary part, and Z2 = c + di, where c is the real part, and d is the imaginary part. We have Z1 * Z2 = (a + bi)(c + di) = ( ac + adi + cbi - bd ). Now, we separate the real and the imaginary part, the real part here is everything without i, so ac - bd, and the imaginary part would be ad + cb. Now, use that in the terms of your class members, and you would get something like this:
const ComplexNumber operator* (const ComplexNumber &rhs)
{
ComplexNumber result;
result.real = real * rhs.real - imaginary * rhs.imaginary;
result.imaginary = real * rhs.imaginary + imaginary * rhs.real;
return result;
}