# 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-
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));
}

```

#### SEEALSO

```   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 4.09 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)
```

## Opportunity

Personal Opportunity - Free software gives you access to billions of dollars of software at no cost. Use this software for your business, personal use or to develop a profitable skill. Access to source code provides access to a level of capabilities/information that companies protect though copyrights. Open source is a core component of the Internet and it is available to you. Leverage the billions of dollars in resources and capabilities to build a career, establish a business or change the world. The potential is endless for those who understand the opportunity.

Business Opportunity - Goldman Sachs, IBM and countless large corporations are leveraging open source to reduce costs, develop products and increase their bottom lines. Learn what these companies know about open source and how open source can give you the advantage.

## Free Software

Free Software provides computer programs and capabilities at no cost but more importantly, it provides the freedom to run, edit, contribute to, and share the software. The importance of free software is a matter of access, not price. Software at no cost is a benefit but ownership rights to the software and source code is far more significant.

Free Office Software - The Libre Office suite provides top desktop productivity tools for free. This includes, a word processor, spreadsheet, presentation engine, drawing and flowcharting, database and math applications. Libre Office is available for Linux or Windows.

## Free Books

The Free Books Library is a collection of thousands of the most popular public domain books in an online readable format. The collection includes great classical literature and more recent works where the U.S. copyright has expired. These books are yours to read and use without restrictions.

Source Code - Want to change a program or know how it works? Open Source provides the source code for its programs so that anyone can use, modify or learn how to write those programs themselves. Visit the GNU source code repositories to download the source.

## Education

Study at Harvard, Stanford or MIT - Open edX provides free online courses from Harvard, MIT, Columbia, UC Berkeley and other top Universities. Hundreds of courses for almost all major subjects and course levels. Open edx also offers some paid courses and selected certifications.

Linux Manual Pages - A man or manual page is a form of software documentation found on Linux/Unix operating systems. Topics covered include computer programs (including library and system calls), formal standards and conventions, and even abstract concepts.