# 14.6. A function on `Complex`

numbers¶

A natural operation we might want to perform on complex numbers is addition. If the numbers are in Cartesian coordinates, addition is easy: you just add the real parts together and the imaginary parts together. If the numbers are in polar coordinates, it is easiest to convert them to Cartesian coordinates and then add them.

Again, it is easy to deal with these cases if we use the accessor functions:

```
Complex add (Complex& a, Complex& b)
{
double real = a.getReal() + b.getReal();
double imag = a.getImag() + b.getImag();
Complex sum (real, imag);
return sum;
}
```

Notice that the arguments to `add`

are not `const`

because they
might be modified when we invoke the accessors. To invoke this function,
we would pass both operands as arguments:

```
Complex c1 (2.0, 3.0);
Complex c2 (3.0, 4.0);
Complex sum = add (c1, c2);
sum.printCartesian();
```

The output of this program is

```
5 + 7i
```

The active code below uses the `add`

function for `Complex`

objects.
As an exercise, write the `subtract`

function for `Complex`

objects
in the commented area of the active code. If you get stuck, you can reveal
the extra problem at the end for help. Once you are finished, feel
free to modify the code and experiment around!

Let’s write the code for the `subtract`

function,
which should return the difference of two `Complex`

objects.

- 3.1i + 1.9i
- Incorrect! Try using the active code above.
- 1.9i + 3.1
- Incorrect! Try using the active code above.
- 3.0 + 1.9i
- Incorrect! Try using the active code above.
- 3.1 + 1.9i
- Correct!

Q-3: What is the correct output of the code below?

```
int main() {
Complex c1 (2.5, 1.3);
Complex c2 (3.9, 4.4);
Complex c3 (9.5, 7.6);
Complex sum = add (c1, c2);
Complex diff = subtract(c3, sum);
diff.printCartesian();
}
```