complex(7) — Linux manual page

NAME | SYNOPSIS | DESCRIPTION | EXAMPLES | SEE ALSO | COLOPHON

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

NAME         top

       complex - basics of complex mathematics

SYNOPSIS         top

       #include <complex.h>

DESCRIPTION         top

       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.

EXAMPLES         top

       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\n", creal(z), cimag(z));
       }

SEE ALSO         top

       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         top

       This page is part of release 5.13 of the Linux man-pages project.
       A description of the project, information about reporting bugs,
       and the latest version of this page, can be found at
       https://www.kernel.org/doc/man-pages/.

                               2021-03-22                     COMPLEX(7)

Pages that refer to this page: cabs(3)cacos(3)cacosh(3)carg(3)casin(3)casinh(3)catan(3)catanh(3)ccos(3)ccosh(3)cexp2(3)cexp(3)cimag(3)clog10(3)clog2(3)clog(3)conj(3)cpow(3)cproj(3)creal(3)csin(3)csinh(3)csqrt(3)ctan(3)ctanh(3)