{ "content": [ { "type": "text", "text": "# COMPLEX (man)\n\n## NAME\n\ncomplex - basics of complex mathematics\n\n## DESCRIPTION\n\nComplex numbers are numbers of the form z = a+b*i, where a and b are real numbers and i =\nsqrt(-1), so that i*i = -1.\n\n## Sections\n\n- **NAME**\n- **SYNOPSIS** (1 subsections)\n- **DESCRIPTION**\n- **EXAMPLES**\n- **SEE ALSO**\n- **COLOPHON**\n\nUse structuredContent.sections for detailed options, examples, and full documentation.\n" } ], "structuredContent": { "command": "COMPLEX", "section": "", "mode": "man", "summary": "complex - basics of complex mathematics", "synopsis": "", "tldr_summary": null, "tldr_examples": [], "tldr_source": null, "flags": [], "examples": [ "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 /* for atan */", "#include ", "#include ", "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": [ { "name": "cabs", "section": "3", "url": "https://www.chedong.com/phpMan.php/man/cabs/3/json" }, { "name": "cacos", "section": "3", "url": "https://www.chedong.com/phpMan.php/man/cacos/3/json" }, { "name": "cacosh", "section": "3", "url": "https://www.chedong.com/phpMan.php/man/cacosh/3/json" }, { "name": "carg", "section": "3", "url": "https://www.chedong.com/phpMan.php/man/carg/3/json" }, { "name": "casin", "section": "3", "url": "https://www.chedong.com/phpMan.php/man/casin/3/json" }, { "name": "casinh", "section": "3", "url": "https://www.chedong.com/phpMan.php/man/casinh/3/json" }, { "name": "catan", "section": "3", "url": "https://www.chedong.com/phpMan.php/man/catan/3/json" }, { "name": "catanh", "section": "3", "url": "https://www.chedong.com/phpMan.php/man/catanh/3/json" }, { "name": "ccos", "section": "3", "url": "https://www.chedong.com/phpMan.php/man/ccos/3/json" }, { "name": "ccosh", "section": "3", "url": "https://www.chedong.com/phpMan.php/man/ccosh/3/json" }, { "name": "cerf", "section": "3", "url": "https://www.chedong.com/phpMan.php/man/cerf/3/json" }, { "name": "cexp", "section": "3", "url": "https://www.chedong.com/phpMan.php/man/cexp/3/json" }, { "name": "cexp2", "section": "3", "url": "https://www.chedong.com/phpMan.php/man/cexp2/3/json" }, { "name": "cimag", "section": "3", "url": "https://www.chedong.com/phpMan.php/man/cimag/3/json" }, { "name": "clog", "section": "3", "url": "https://www.chedong.com/phpMan.php/man/clog/3/json" }, { "name": "clog10", "section": "3", "url": "https://www.chedong.com/phpMan.php/man/clog10/3/json" }, { "name": "clog2", "section": "3", "url": "https://www.chedong.com/phpMan.php/man/clog2/3/json" }, { "name": "conj", "section": "3", "url": "https://www.chedong.com/phpMan.php/man/conj/3/json" }, { "name": "cpow", "section": "3", "url": "https://www.chedong.com/phpMan.php/man/cpow/3/json" }, { "name": "cproj", "section": "3", "url": "https://www.chedong.com/phpMan.php/man/cproj/3/json" }, { "name": "creal", "section": "3", "url": "https://www.chedong.com/phpMan.php/man/creal/3/json" }, { "name": "csin", "section": "3", "url": "https://www.chedong.com/phpMan.php/man/csin/3/json" }, { "name": "csinh", "section": "3", "url": "https://www.chedong.com/phpMan.php/man/csinh/3/json" }, { "name": "csqrt", "section": "3", "url": "https://www.chedong.com/phpMan.php/man/csqrt/3/json" }, { "name": "ctan", "section": "3", "url": "https://www.chedong.com/phpMan.php/man/ctan/3/json" }, { "name": "ctanh", "section": "3", "url": "https://www.chedong.com/phpMan.php/man/ctanh/3/json" } ], "section_outline": [ { "name": "NAME", "lines": 2, "subsections": [] }, { "name": "SYNOPSIS", "lines": 1, "subsections": [ { "name": "#include ", "lines": 1 } ] }, { "name": "DESCRIPTION", "lines": 20, "subsections": [] }, { "name": "EXAMPLES", "lines": 16, "subsections": [] }, { "name": "SEE ALSO", "lines": 4, "subsections": [] }, { "name": "COLOPHON", "lines": 7, "subsections": [] } ], "sections": { "NAME": { "content": "complex - basics of complex mathematics\n", "subsections": [] }, "SYNOPSIS": { "content": "", "subsections": [ { "name": "#include ", "content": "" } ] }, "DESCRIPTION": { "content": "Complex numbers are numbers of the form z = a+b*i, where a and b are real numbers and i =\nsqrt(-1), so that i*i = -1.\n\nThere are other ways to represent that number. The pair (a,b) of real numbers may be viewed\nas a point in the plane, given by X- and Y-coordinates. This same point may also be de‐\nscribed by giving the pair of real numbers (r,phi), where r is the distance to the origin O,\nand phi the angle between the X-axis and the line Oz. Now z = r*exp(i*phi) =\nr*(cos(phi)+i*sin(phi)).\n\nThe basic operations are defined on z = a+b*i and w = c+d*i as:\n\naddition: z+w = (a+c) + (b+d)*i\n\nmultiplication: z*w = (a*c - b*d) + (a*d + b*c)*i\n\ndivision: z/w = ((a*c + b*d)/(c*c + d*d)) + ((b*c - a*d)/(c*c + d*d))*i\n\nNearly all math function have a complex counterpart but there are some complex-only func‐\ntions.\n", "subsections": [] }, "EXAMPLES": { "content": "Your C-compiler can work with complex numbers if it supports the C99 standard. Link with\n-lm. The imaginary unit is represented by I.\n\n/* check that exp(i * pi) == -1 */\n#include /* for atan */\n#include \n#include \n\nint\nmain(void)\n{\ndouble pi = 4 * atan(1.0);\ndouble complex z = cexp(I * pi);\nprintf(\"%f + %f * i\\n\", creal(z), cimag(z));\n}\n", "subsections": [] }, "SEE ALSO": { "content": "cabs(3), cacos(3), cacosh(3), carg(3), casin(3), casinh(3), catan(3), catanh(3), ccos(3),\nccosh(3), cerf(3), cexp(3), cexp2(3), cimag(3), clog(3), clog10(3), clog2(3), conj(3),\ncpow(3), cproj(3), creal(3), csin(3), csinh(3), csqrt(3), ctan(3), ctanh(3)\n", "subsections": [] }, "COLOPHON": { "content": "This page is part of release 5.10 of the Linux man-pages project. A description of the\nproject, information about reporting bugs, and the latest version of this page, can be found\nat https://www.kernel.org/doc/man-pages/.\n\n\n\n2020-06-09 COMPLEX(7)", "subsections": [] } } } }