COMPLEX(7)						     Linux Programmer's Manual							COMPLEX(7)

NAME

       complex - basics of complex mathematics

SYNOPSIS

       #include <complex.h>

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-
       coordinates.  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 <math.h>	/* for atan */
       #include <stdio.h>
       #include <complex.h>

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

SEE ALSO

       cabs(3),  cacos(3),  cacosh(3), carg(3), casin(3), casinh(3), catan(3), catanh(3), ccos(3), ccosh(3), cerf(3), cexp(3), cexp2(3), cimag(3),
       clog(3), clog10(3), clog2(3), conj(3), cpow(3), cproj(3), creal(3), csin(3), csinh(3), csqrt(3), ctan(3), ctanh(3)

COLOPHON

       This page is part of release 3.53 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/.

								    2011-09-16								COMPLEX(7)