Chapter 18: Library Features Added by C99

The complex Class

The header <complex> defines the complex class, which represents complex numbers. It also defines a series of functions and operators that operate on objects of type complex.

The template specification for complex is shown here:

        template <class T> class complex

Here, T specifies the type used to store the components of a complex number. There are three predefined specializations of complex:

       class complex<float>
       class complex<double>
       class complex<long double>

The complex class has the following constructors:

        complex(const T &real = T( ), const T = &imaginary = T( ));
        complex(const complex &ob);
        template <class T1> complex(const complex<T1> &ob);

The first constructs a complex object with a real component of real and an imaginary component of imaginary. These values default to zero if not specified. The second creates a copy of ob. The third creates a complex object from ob.

The following operations are defined for complex objects:

+	–	*	/
– =	+=	/=	*=
=	==	!=

The nonassignment operators are overloaded three ways: once for operations involving a complex object on the left and a scalar object on the right, again for operations involving a scalar on the left and a complex object on the right, and finally for operations involving two complex objects. For example, the following types of operations are allowed:

      complex_ob + scalar
      scalar + complex_ob
      complex_ob + complex_ob

Operations involving scalar quantities affect only the real component.

Two member functions are defined for complex: real( ) and imag( ). They are shown here:

     T real( ) const;
     T imag( ) const;

The real( ) function returns the real component of the invoking object and imag( ) returns the imaginary component. The following functions are also defined for complex objects:

Function	Description
template <class T>   T abs(const complex<T> &ob);	Returns the absolute value of ob
template <class T>   T arg(const complex<T> &ob);	Returns the phase angle of ob
template <class T> complex<T>   conj(const complex<T> &ob);	Returns the conjugate of ob
template <class T>   complex<T> cos(const complex<T> &ob);	Returns the cosine of ob
template <class T>   complex<T>      cosh(const complex<T> &ob);	Returns the hyperbolic cosine of ob
template <class T>   complex<T>      exp(const complex<T> &ob);	Returns the eob
template <class T>   T imag(const complex<T> &ob);	Returns the imaginary component of ob
template <class T>   complex<T>      log(const complex<T> &ob);	Returns the natural logarithm of ob
template <class T>   complex<T>      log10(const complex<T> &ob);	Returns the base 10 logarithm of ob
template <class T>   T norm(const complex<T> &ob);	Returns the magnitude of ob squared
template <class T>   complex<T>      polar(const T &v, const T &theta=0);	Returns a complex number that has the magnitude specified by v and a phase angle of theta
template <class T>   complex<T>      pow(const complex<T> &b, int e);	Returns be
template <class T>   complex<T>      pow(const complex<T> &b,               const T &e);	Returns be
template <class T>   complex<T>      pow(const complex<T> &b,               const complex<T> &e);	Returns be
template <class T>   complex<T>      pow(const T &b,               const complex<T> &e);	Returns be
template <class T>   T real(const complex<T> &ob);	Returns the real component of ob
template <class T>   complex<T> sin(const complex<T> &ob);	Returns the sine of ob
template <class T>   complex<T>      sinh(const complex<T> &ob);	Returns the hyperbolic sine of ob
template <class T>   complex<T>      sqrt(const complex<T> &ob);	Returns the square root of ob
template <class T>   complex<T>      tan(const complex<T> &ob);	Returns the tangent of ob
template <class T>   complex<T>      tanh(const complex<T> &ob);	Returns the hyperbolic tangent of ob