SIMPLE SOLUTIONS

COMPLEX - reference manual online

Basics of complex mathematics.

Chapter
2011-09-16
COMPLEX(7)                          Linux Programmer's Manual                          COMPLEX(7)

NAME complex - basics of complex mathematics
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 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 func‐ tions.
EXAMPLE 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 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 4.04 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 http://www.kernel.org/doc/man-pages/.
2011-09-16 COMPLEX(7)
This manual Reference Other manuals
complex(7) referred by cabs(3) | cacos(3) | cacosh(3) | carg(3) | casin(3) | casinh(3) | catan(3) | catanh(3) | ccos(3) | ccosh(3) | cexp(3) | cexp2(3) | cimag(3) | clog(3) | clog10(3) | clog2(3) | conj(3) | cpow(3) | cproj(3) | creal(3)
refer to cabs(3) | cacos(3) | cacosh(3) | carg(3) | casin(3) | casinh(3) | catan(3) | catanh(3) | ccos(3) | ccosh(3) | cexp(3) | cexp2(3) | cimag(3) | clog(3) | clog10(3) | clog2(3) | conj(3) | cpow(3) | cproj(3) | creal(3)