# COMPLEX - man(7) - [phpMan]

[_complex_(7)](https://www.chedong.com/phpMan.php/man/complex/7/markdown)                        Miscellaneous Information Manual                        [_complex_(7)](https://www.chedong.com/phpMan.php/man/complex/7/markdown)

## NAME
       complex - basics of complex mathematics

## LIBRARY
       Math library (_libm_, _-lm_)

## 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 de‐
       scribed 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  func‐
       tions.

## EXAMPLES
       Your C-compiler can work with complex numbers if it supports the C99 standard.  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)](https://www.chedong.com/phpMan.php/man/cabs/3/markdown),  [**cacos**(3)](https://www.chedong.com/phpMan.php/man/cacos/3/markdown),  [**cacosh**(3)](https://www.chedong.com/phpMan.php/man/cacosh/3/markdown),  [**carg**(3)](https://www.chedong.com/phpMan.php/man/carg/3/markdown),  [**casin**(3)](https://www.chedong.com/phpMan.php/man/casin/3/markdown), [**casinh**(3)](https://www.chedong.com/phpMan.php/man/casinh/3/markdown), [**catan**(3)](https://www.chedong.com/phpMan.php/man/catan/3/markdown), [**catanh**(3)](https://www.chedong.com/phpMan.php/man/catanh/3/markdown), [**ccos**(3)](https://www.chedong.com/phpMan.php/man/ccos/3/markdown),
       [**ccosh**(3)](https://www.chedong.com/phpMan.php/man/ccosh/3/markdown), [**cerf**(3)](https://www.chedong.com/phpMan.php/man/cerf/3/markdown),  [**cexp**(3)](https://www.chedong.com/phpMan.php/man/cexp/3/markdown),  [**cexp2**(3)](https://www.chedong.com/phpMan.php/man/cexp2/3/markdown),  [**cimag**(3)](https://www.chedong.com/phpMan.php/man/cimag/3/markdown),  [**clog**(3)](https://www.chedong.com/phpMan.php/man/clog/3/markdown),  [**clog10**(3)](https://www.chedong.com/phpMan.php/man/clog10/3/markdown),  [**clog2**(3)](https://www.chedong.com/phpMan.php/man/clog2/3/markdown),  [**conj**(3)](https://www.chedong.com/phpMan.php/man/conj/3/markdown),
       [**cpow**(3)](https://www.chedong.com/phpMan.php/man/cpow/3/markdown), [**cproj**(3)](https://www.chedong.com/phpMan.php/man/cproj/3/markdown), [**creal**(3)](https://www.chedong.com/phpMan.php/man/creal/3/markdown), [**csin**(3)](https://www.chedong.com/phpMan.php/man/csin/3/markdown), [**csinh**(3)](https://www.chedong.com/phpMan.php/man/csinh/3/markdown), [**csqrt**(3)](https://www.chedong.com/phpMan.php/man/csqrt/3/markdown), [**ctan**(3)](https://www.chedong.com/phpMan.php/man/ctan/3/markdown), [**ctanh**(3)](https://www.chedong.com/phpMan.php/man/ctanh/3/markdown)

Linux man-pages 6.7                          2023-10-31                                   [_complex_(7)](https://www.chedong.com/phpMan.php/man/complex/7/markdown)