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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) + (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 <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), 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

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       project,  and information about reporting bugs, can be found at http://man7.org/linux/man-
       pages/.

                                            2011-09-16                                 COMPLEX(7)