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!

#include <iostream>
#include <cmath>
using namespace std;

class Complex
{
  double real, imag;
  double mag, theta;
  bool cartesian, polar;

public:
  Complex ();
  Complex (double r, double i);
  void calculateCartesian ();
  double getReal ();
  double getImag ();
  void calculatePolar ();
  double getMag ();
  double getTheta ();
  void printCartesian ();
  void printPolar ();
};

Complex add (Complex& a, Complex& b);
Complex subtract (Complex& a, Complex& b) {
  // ``subtract`` should subtract b from a and return
  // the difference of the two ``Complex`` objects.
  // Delete the existing code and write your implementation here.
  Complex c (0,0); return c;
}

int main() {
  Complex c1 (2.0, 3.0);
  Complex c2 (3.0, 4.0);
  Complex sum = add (c1, c2);
  sum.printCartesian();

// Difference should be 1 + 1i
  Complex diff = subtract(c2, c1);
  diff.printCartesian();
}
====
Complex::Complex () { cartesian = false;  polar = false; }

Complex::Complex (double r, double i) {
  real = r;  imag = i;
  cartesian = true;  polar = false;
}

void Complex::calculateCartesian () {
  real = mag * cos (theta);
  imag = mag * sin (theta);
  cartesian = true;
}

double Complex::getReal () {
  if (cartesian == false) calculateCartesian ();
  return real;
}

double Complex::getImag () {
  if (cartesian == false) calculateCartesian ();
  return imag;
}

void Complex::calculatePolar () {
  mag = sqrt(pow(real, 2) + pow(imag, 2));
  theta = atan(imag / real);
  polar = true;
}

double Complex::getMag () {
  if (polar == false) {
    calculatePolar ();
  }
  return mag;
}

double Complex::getTheta () {
  if (polar == false) {
    calculatePolar ();
  }
  return theta;
}

void Complex::printCartesian () {
  cout << getReal() << " + " << getImag() << "i" << endl;
}

void Complex::printPolar () {
  cout << getMag() << " e^ " << getTheta() << "i" << endl;
}

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

Let’s write the code for the subtract function, which should return the difference of two Complex objects.

        Complex subtract (Complex& a, Complex& b) {
---
Complex subtract (Complex& a) {                         #paired
---
   double real = a.getReal() - b.getReal();
---
   double real = a.getReal() + b.getReal();                         #paired
---
   double imag = a.getImag() - b.getImag();
---
   Complex diff (real, imag);
---
   Complex diff (imag, real);                         #paired
---
   return diff;
}
---
   return sum;                         #paired
}

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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();
}

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!

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14.6. A function on Complex numbers¶

Before you keep reading...

Before you keep reading...

14.6. A function on `Complex` numbers¶