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), carg(3), cexp(3), cimag(3), creal(3)COLOPHONThis page is part of release 3.22 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/. 2009-07-25 COMPLEX(7)

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