complex

Section: Environments, Tables, and Troff Macros (7)
Updated: 202-0-08
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NAME

complex - basics of complex mathematics  

LIBRARY

Math library (libm,~-lm)  

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 - and -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 -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 comple-only functions.

 

EXAMPLES

Your -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[rs]n", 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)

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Index

NAME

LIBRARY

SYNOPSIS

DESCRIPTION

EXAMPLES

SEE ALSO