complex(7) — Linux manual page


complex(7)          Miscellaneous Information Manual          complex(7)

NAME         top

       complex - basics of complex mathematics

LIBRARY         top

       Math library (libm, -lm)

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 +

       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.  The imaginary unit is represented by I.

       /* check that exp(i * pi) == -1 */
       #include <math.h>        /* for atan */
       #include <stdio.h>
       #include <complex.h>

           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)

Linux man-pages (unreleased)     (date)                       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)