Implementation of complx class?

// Complx.h
#include <iostream>
#include <fstream>
using namespace std;

class complx
{
double real,
imag;
public:
complx( double real = 0., double imag = 0.); // constructor
complx operator+(complx); // operator+()

complx operator+(double); // operator+()with double
complx operator- (complx); // operator-()
complx operator* (complx); // operator*()

bool operator== (complx); // operator==()


//Sets private data members.
void Set(double new_real, double new_imaginary) {
real = new_real;
imag = new_imaginary;
}

//Returns the real part of the complex number.
double Real() {
return real;
}

//Returns the imaginary part of the complex number.
double Imaginary() {
return imag;
}
};

ostream &operator << ( ostream &out_file, complx number );

extern istream &operator >> ( istream &in_file, complx &number );

extern ifstream &operator >> ( ifstream &in_file, complx &number );

complx &operator + (double, complx);
complx &operator - (double, complx);
complx &operator * (double, complx);

// Complx.cpp
#include "complx.h"
// define I/O stream

extern ifstream &operator >> ( ifstream &in_file, complx &number )
{
double re, is;
char ch;
if (in_file >> ch && ch == '('&& in_file >> re >> ch && ch == ','
&& in_file >> is >> ch && ch == ')')
number.Set(re,is);
else cerr << "Finish the input"<<endl;
return in_file;
}

ostream &operator<< ( ostream &out_file, complx number )
{
out_file << '(' << number.Real() << ',' << number.Imaginary() << ')';
return out_file;
}

// define constructor
complx::complx( double r, double i )
{
real = r; imag = i;
}

// define overloaded + (plus) operator
complx complx:perator+ (complx c)
{
complx result;
result.real = (this->real + c.real);
result.imag = (this->imag + c.imag);
return result;
}

//call_complx.cpp
#include "complx.h"
ifstream infile ("in.dat");
int main()
{
int i=0;
complx in[7];
double d = 4.5; 
cout<< "The input numbers are: " << endl;

while (infile >> in[i]){
cout << in[i] << endl;
i++;
} 
complx s1 = in[0] + in[1]; // calls complx:perator+()
complx s2 = d + in[2]; // overload operator+()
complx s3 = in[3] + d; // overload operator+()
complx a = in[4] - in[5];
complx mm=in[3]*in[4];
complx dm=d*in[4] ;
complx b=d-in[0] ;

cout << "The sum is a complex number " << s1 <<endl;
cout << "The sum is a complex number " << s2 <<endl;
cout << "The sum is a complex number " << s3 <<endl;
cout << "The subtract is a complex number " << a <<endl;
cout << "The product is a complex number " << mm <<endl; 
cout << "The subtract is a complex number " << b <<endl;
cout << "The product is a complex number " << dm <<endl;
if (in[4] == in[5]) cout << "in[4] and in[5] are the same " << endl;
system("pause");
return 0; //successful termination
}