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man:complex

COMPLEX(7) Linux Programmer's Manual COMPLEX(7)

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-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 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)); }```

```     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

```     This  page  is  part of release 4.16 of the Linux man-pages project.  A
description of the project, information about reporting bugs,  and  the
latest     version     of     this    page,    can    be    found    at
https://www.kernel.org/doc/man-pages/.```
`                                2011-09-16                        COMPLEX(7)`