COMPLEX(7)		   Linux Programmers Manual		   COMPLEX(7)



NAME
       complex - basics of complex mathematics

SYNOPSIS
       #include 

DESCRIPTION
       Complex	numbers  are  numbers of the form z = a+b*i, where a and b are
       real numbers and i = sqrt(-1), so that i*i = -1.
       There are other ways to represent that number.  The pair (a,b) of  real
       numbers	may be viewed as a point in the plane, given by X- and Y-coor
       dinates.  This same point may also be described by giving the  pair  of
       real  numbers (r,phi), where r is the distance to the origin O, and phi
       the angle between the X-axis and the line Oz.  Now z =  r*exp(i*phi)  =
       r*(cos(phi)+i*sin(phi)).

       The basic operations are defined on z = a+b*i and w = c+d*i as:

       addition: z+w = (a+c) + (b+d)*i

       multiplication: z*w = (a*c - b*d) + (a*d + b*c)*i

       division: z/w = ((a*c + b*d)/(c*c + d*d)) + ((b*c - a*d)/(c*c + d*d))*i

       Nearly  all math function have a complex counterpart but there are some
       complex-only functions.

EXAMPLE
       Your C-compiler can work with complex numbers if it  supports  the  C99
       standard.  Link with -lm.  The imaginary unit is represented by I.

       /* check that exp(i * pi) == -1 */
       #include 	/* for atan */
       #include 

       int
       main(void)
       {
	   double pi = 4 * atan(1.0);
	   complex z = cexp(I * pi);
	   printf("%f + %f * i\n", creal(z), cimag(z));
       }

SEE ALSO
       cabs(3), carg(3), cexp(3), cimag(3), creal(3)

COLOPHON
       This  page  is  part of release 3.05 of the Linux man-pages project.  A
       description of the project, and information about reporting  bugs,  can
       be found at http://www.kernel.org/doc/man-pages/.



				  2002-07-28			    COMPLEX(7)