COMPLEX
NAME
SYNOPSIS
DESCRIPTION
EXAMPLES
SEE ALSO
COLOPHON
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-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
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 bodies manpages.csv script_extrae_body.sh script.sh usr pi) == −1 bodies/ usr/
#include
#include
#include
int
main(void)
{
double pi = 4 bodies manpages.csv script_extrae_body.sh script.sh usr atan(1.0);
double complex z = cexp(I bodies manpages.csv script_extrae_body.sh script.sh usr pi);
printf(“%f + %f bodies manpages.csv script_extrae_body.sh script.sh usr in”, 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 5.10 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/.