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-coor‐ dinates. 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. 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
/* for atan */ #include
#include
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 3.53 of the Linux man-pages project. A description of the project, and information about reporting bugs, can
be found at http://www.kernel.org/doc/man-pages/.
2011-09-16 COMPLEX(7)