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complex(5) - complex, complex - basics of complex mathematics - man 5 complex

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COMPLEX(5)                       complex math                       COMPLEX(5)



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(1,8) 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(3,n) 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 <complex.h>
       main() {
            double pi = 4*atan(1);
            complex z = cexp(I*pi);
            printf(1,3,1 builtins)("%f+%f*i\n", creal(z), cimag(z));
       }

SEE ALSO
       cabs(3), carg(3), cexp(3), cimag(3), creal(3)



                                  2002-07-28                        COMPLEX(5)

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