#include <iostream>
#include <cmath>

struct complex
{ double real, imag;

  complex();
  complex(double r, double i);

  void print();
  double magnitude();
  void add(const complex & x);
  void sub(const complex & x);
  void mul(const complex & x);
  void div(const complex & x); };


struct fraction
{ int top, bot;

  fraction();
  fraction(int t, int b);

  void print();
  double magnitude();
  void normalise();
  void add(const fraction & x);
  void sub(const fraction & x);
  void mul(const fraction & x);
  void div(const fraction & x); };


void main()
{ fraction a;
  fraction b(3, 7);
  fraction c(2, 9);
  fraction d(7, 8);

  b.print(); cout << " * "; c.print(); cout << " + "; d.print(); cout << " = ";
  b.mul(c);
  b.add(d);
  b.print();
  cout << "\n";

  b.print(); cout << " + "; d.print(); cout << " = ";
  b.add(d);
  b.print(); cout << ", magnitude = " << b.magnitude() << "\n";


  complex x(1, 3);
  complex y(2, -1);
  complex z(1, 1);

  x.print(); cout << " * "; y.print(); cout << " + "; z.print(); cout << " = ";
  x.mul(y);
  x.add(z);
  x.print();
  cout << "\n";

  x.print(); cout << " + "; z.print(); cout << " = ";
  x.add(z);
  x.print(); cout << ", magnitude = " << x.magnitude() << "\n"; }

  

complex::complex()
{ real = 0.0;
  imag = 0.0; }

complex::complex(double r, double i)
{ real = r;
  imag = i; }

void complex::print()
{ cout << real;
  if (imag >= 0.0)
    cout << "+";
  cout << imag << "i"; }

double complex::magnitude()
{ return sqrt(real*real + imag*imag); }

void complex::add(const complex & x)
{ real = real + x.real;
  imag = imag + x.imag; }

void complex::sub(const complex & x)
{ real = real - x.real;
  imag = imag - x.imag; }

void complex::mul(const complex & x)
{ real = real * x.real - imag * x.imag;
  imag = real * x.imag + imag * x.real; }

void complex::div(const complex & x)
{ double d = x.real * x.real + x.imag * x.imag;
  real = (real * x.real + imag * x.imag) / d;
  imag = (imag * x.real - real * x.imag) / d; }

fraction::fraction()
{ top = 0;
  bot = 1; }

fraction::fraction(int t, int b)
{ top = t;
  bot = b; }

void fraction::print()
{ cout << top << "/" << bot; }

double fraction::magnitude()
{ return (double)top / (double)bot; }

void fraction::normalise()
{ int gcd = top, b = bot;
  while (b != 0)
  { int t = gcd % b;
    gcd = b; 
    b = t; }
  top /= gcd;
  bot /= gcd; }

void fraction::add(const fraction & x)
{ top = top * x.bot + bot * x.top;
  bot = bot * x.bot;
  normalise(); }

void fraction::sub(const fraction & x)
{ top = top * x.bot - bot * x.top;
  bot = bot * x.bot;
  normalise(); }

void fraction::mul(const fraction & x)
{ top = top * x.top;
  bot = bot * x.bot;
  normalise(); }

void fraction::div(const fraction & x)
{ top = top * x.bot;
  bot = bot * x.top;
  normalise(); }