P6.1       The interface for the Complex class is provided below (Note that the first letter of Complex is capitalized in order to distinguish it from the complex class defined in <complex> header file). A complex number c is defined as c = a + bi where c is the complex number consisting of two part: real part denoted by ‘a’ and an imaginary part denoted by ‘b’ multiplied by i and  i =  . (The website at https://en.wikipedia.org/wiki/Complex_number provides an introductory level discussion of complex numbers.) Operations such as addition, subtraction, multiplication, and division can be performed on complex number in a way similar to the operations performed on rational numbers since computations only involve a and b, which are real numbers. For you convenience, the basic four operations or computations are provided below. Note that all four computations involve only real numbers (double type in C++), this program is very similar to the rational number problem.

Addition:                              

Subtraction:                

Multiplication:                       

Division:                     

where i = ; it does not even enter into your program code.

classComplex

{

   friendostream&operator<<(ostream&out, constComplex&cobj);

        // Postcondition: contents of cobj is display in (a, b) format, e.g., 3 - 4i ==> (3, -4)

   friendistream&operator>>(istream&out, Complex&cobj);

   // prompt message "Enter real and imaginary values: " is displayed in main() by the client of the class

        // Postconodition: two values entered by the users are assinged to real and imag of cobj, respectively

public:

   Complex();

   // default constructor

   Complex(doubler, doublei);

        // Postcondition: a complex object is declared and initialized to (r, i) or (0, 0) if no values are passed to the constructor

   void setComplexNumber(doublea, doubleb);

   // a mutator function

        // Postcondition: set the real and imaginary parts of the calling complex object to a and b, respectively

   Complexoperator+(constComplex&c2) const;

   // Postcondition: sum of (*this) - c2 is returned

   Complexoperator-(constComplex&c2) const;

   // Postcondition: difference of (*this) - c2 is returned

   Complexoperator*(constComplex&c2) const;

   // Postcondition: product of (*this) * c2 is returned

   Complexoperator/(constComplex&c2) const;

   // Postcondition: quotient of (*this) / c2 is returned

   booloperator==(constComplex&c2) const;

   // Postcondition: returns true if (*this == c2) is true; returns false otherwise

private:

   double real;     // real part of a complex number (a, b)

   double imag;     // imaginary part of a complex number (a, b)

};

1.       You are asked to implement all the member and non-member functions.

2.       Write a main() function to  test all the above functions.The output should be similar to the following sample display:

P6.2       (Optional) The interface for the String class (notice that the first letter of String in capitalized to distinguish it from the “string” class defined by C++ in <string> header file) is provide below.

classString

{

   friendostream&operator<<(ostream&, constString&obj);

   // Postcondition: output/display sobj

   friendistream&operator>>(istream&, String&sobj);

   // Client of this function prompts the user to enter a string

   // Postcondition: input values from the user to initialize sobj

public:

   String(constchar* = "");

   // Default constructor

   String(constString&sobj);

   // copy constructor

   // Postcondition: newly created object is initialized with values from sobj

   ~String();

   // destructor

   constString&operator=(constString&sobj);

   // Postcondition: calling object gets the values of sobj

   constString&operator+=(constString&sobj);

   // Postcondition: sum/concatenation of the calling object and sobj is returned

       bool operator==(constString&sobj) const;

   // Postcondition: return true if calling object == sobj; return false otherwise

   bool operator<(constString&) const;

   // Postcondition: return true if calling object < sobj; return false otherwise

bool operator>(constString&) const;

   // Postcondition: return true if calling object > sobj; return false otherwise

   char operator[](int) const;

   // Postcondition: return true if calling object < sobj; return false otherwise

   int getLength() const;

   // Postcondition: return true if calling object < sobj; return false otherwise

private:

   int length;

   char *sPtr;      // points to a dynamic C-string, which is a null-terminated char array

};

       You are asked to

1.       Implement all member and friend functions

2.       Write a main() function to test all those functions. You are asked to format the outputs to make it easy to read.

·         Note: To carry out this assignment, you may need to use some of the C-string manipulation functions such as strcpy, strcat, strcmp, etc. You may want to visit http://www.cplusplus.com/reference/cstring/for more detailed information.