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NAME | LIBRARY | SYNOPSIS | DESCRIPTION | EXAMPLES | SEE ALSO | COLOPHON |
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complex(7) Miscellaneous Information Manual complex(7)
complex - basics of complex mathematics
Math library (libm, -lm)
#include <complex.h>
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.
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>
int
main(void)
{
double pi = 4 * atan(1.0);
double complex z = cexp(I * pi);
printf("%f + %f * i\n", creal(z), cimag(z));
}
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)
This page is part of the man-pages (Linux kernel and C library
user-space interface documentation) project. Information about
the project can be found at
⟨https://www.kernel.org/doc/man-pages/⟩. If you have a bug report
for this manual page, see
⟨https://git.kernel.org/pub/scm/docs/man-pages/man-pages.git/tree/CONTRIBUTING⟩.
This page was obtained from the tarball man-pages-6.15.tar.gz
fetched from
⟨https://mirrors.edge.kernel.org/pub/linux/docs/man-pages/⟩ on
2025-08-11. If you discover any rendering problems in this HTML
version of the page, or you believe there is a better or more up-
to-date source for the page, or you have corrections or
improvements to the information in this COLOPHON (which is not
part of the original manual page), send a mail to
man-pages@man7.org
Linux man-pages 6.15 2025-05-17 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)
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HTML rendering created 2025-09-06 by Michael Kerrisk, author of The Linux Programming Interface. For details of in-depth Linux/UNIX system programming training courses that I teach, look here. Hosting by jambit GmbH. |
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