COMPLEX(7) (2020-06-09) 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) division: z/w = ((a*c + b*d)/(c*c 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 * 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), Page 1 Plan 9 (printed 5/24/22) COMPLEX(7) (2020-06-09) COMPLEX(7) 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/. Page 2 Plan 9 (printed 5/24/22)