### 5.1 Representation of complex numbers

Complex numbers are represented using the type `gsl_complex`. The internal representation of this type may vary across platforms and should not be accessed directly. The functions and macros described below allow complex numbers to be manipulated in a portable way.

For reference, the default form of the `gsl_complex` type is given by the following struct,

    typedef struct
    {
      double dat[2];
    } gsl_complex;

The real and imaginary part are stored in contiguous elements of a two element array. This eliminates any padding between the real and imaginary parts, `dat[0]` and `dat[1]`, allowing the struct to be mapped correctly onto packed complex arrays.

Function: gsl_complex gsl_complex_rect (double x, double y)

  This function uses the rectangular Cartesian components (x,y) to return the complex number z = x + i y. An inline version of this function is used when `HAVE_INLINE` is defined.

Function: gsl_complex gsl_complex_polar (double r, double theta)

  This function returns the complex number z = r \exp(i \theta) = r (\cos(\theta) + i \sin(\theta)) from the polar representation (r,theta).

Macro: GSL_REAL (z)
Macro: GSL_IMAG (z)

  These macros return the real and imaginary parts of the complex number z.

Macro: GSL_SET_COMPLEX (zp, x, y)

  This macro uses the Cartesian components (x,y) to set the real and imaginary parts of the complex number pointed to by zp. For example,

      GSL_SET_COMPLEX(&z, 3, 4)

  sets z to be 3 + 4i.

Macro: GSL_SET_REAL (zp,x)
Macro: GSL_SET_IMAG (zp,y)

  These macros allow the real and imaginary parts of the complex number pointed to by zp to be set independently.