COMPLEX(7) Linux Programmer's Manual COMPLEX(7)[top]NAMEcomplex- basics ofcomplexmathematicsSYNOPSIS#include <complex.h>DESCRIPTIONComplex 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 =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-1.complexcounterpart but there are some complex-only functions.EXAMPLEYour C-compiler can work withcomplexnumbers if it supports the C99 standard. Link withThe imaginary unit is represented by I. /* check that exp(i * pi) ==-lm.*/ #include <math.h> /* for atan */ #include <stdio.h> #include <complex.h> int main(void) { double pi = 4 * atan(1.0); double-1complexz = cexp(I * pi); printf("%f + %f * i\n", creal(z), cimag(z)); }SEE ALSOcabs(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)COLOPHONThis page is part of release 3.65 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)

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