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# SOME DESCRIPTIVE TITLE
# Copyright (C) YEAR Free Software Foundation, Inc.
# This file is distributed under the same license as the PACKAGE package.
# FIRST AUTHOR <EMAIL@ADDRESS>, YEAR.
#
#, fuzzy
msgid ""
msgstr ""
"Project-Id-Version: PACKAGE VERSION\n"
"POT-Creation-Date: 2024-06-01 05:45+0200\n"
"PO-Revision-Date: YEAR-MO-DA HO:MI+ZONE\n"
"Last-Translator: FULL NAME <EMAIL@ADDRESS>\n"
"Language-Team: LANGUAGE <LL@li.org>\n"
"Language: \n"
"MIME-Version: 1.0\n"
"Content-Type: text/plain; charset=UTF-8\n"
"Content-Transfer-Encoding: 8bit\n"
#. type: TH
#: archlinux debian-bookworm debian-unstable fedora-40 fedora-rawhide
#: mageia-cauldron opensuse-leap-15-6 opensuse-tumbleweed
#, no-wrap
msgid "complex"
msgstr ""
#. type: TH
#: archlinux debian-unstable opensuse-tumbleweed
#, no-wrap
msgid "2024-05-02"
msgstr ""
#. type: TH
#: archlinux debian-unstable
#, no-wrap
msgid "Linux man-pages 6.8"
msgstr ""
#. type: SH
#: archlinux debian-bookworm debian-unstable fedora-40 fedora-rawhide
#: mageia-cauldron opensuse-leap-15-6 opensuse-tumbleweed
#, no-wrap
msgid "NAME"
msgstr ""
#. type: Plain text
#: archlinux debian-bookworm debian-unstable fedora-40 fedora-rawhide
#: mageia-cauldron opensuse-leap-15-6 opensuse-tumbleweed
msgid "complex - basics of complex mathematics"
msgstr ""
#. type: SH
#: archlinux debian-unstable fedora-40 fedora-rawhide mageia-cauldron
#: opensuse-tumbleweed
#, no-wrap
msgid "LIBRARY"
msgstr ""
#. type: Plain text
#: archlinux debian-unstable fedora-40 fedora-rawhide mageia-cauldron
#: opensuse-tumbleweed
msgid "Math library (I<libm>, I<-lm>)"
msgstr ""
#. type: SH
#: archlinux debian-bookworm debian-unstable fedora-40 fedora-rawhide
#: mageia-cauldron opensuse-leap-15-6 opensuse-tumbleweed
#, no-wrap
msgid "SYNOPSIS"
msgstr ""
#. type: Plain text
#: archlinux debian-bookworm debian-unstable fedora-40 fedora-rawhide
#: mageia-cauldron opensuse-leap-15-6 opensuse-tumbleweed
#, no-wrap
msgid "B<#include E<lt>complex.hE<gt>>\n"
msgstr ""
#. type: SH
#: archlinux debian-bookworm debian-unstable fedora-40 fedora-rawhide
#: mageia-cauldron opensuse-leap-15-6 opensuse-tumbleweed
#, no-wrap
msgid "DESCRIPTION"
msgstr ""
#. type: Plain text
#: archlinux debian-bookworm debian-unstable fedora-40 fedora-rawhide
#: mageia-cauldron opensuse-leap-15-6 opensuse-tumbleweed
msgid ""
"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."
msgstr ""
#. type: Plain text
#: archlinux debian-bookworm debian-unstable fedora-40 fedora-rawhide
#: mageia-cauldron opensuse-leap-15-6 opensuse-tumbleweed
msgid ""
"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))."
msgstr ""
#. type: Plain text
#: archlinux debian-bookworm debian-unstable fedora-40 fedora-rawhide
#: mageia-cauldron opensuse-leap-15-6 opensuse-tumbleweed
msgid "The basic operations are defined on z = a+b*i and w = c+d*i as:"
msgstr ""
#. type: TP
#: archlinux debian-bookworm debian-unstable fedora-40 fedora-rawhide
#: mageia-cauldron opensuse-leap-15-6 opensuse-tumbleweed
#, no-wrap
msgid "B<addition: z+w = (a+c) + (b+d)*i>"
msgstr ""
#. type: TP
#: archlinux debian-bookworm debian-unstable fedora-40 fedora-rawhide
#: mageia-cauldron opensuse-leap-15-6 opensuse-tumbleweed
#, no-wrap
msgid "B<multiplication: z*w = (a*c - b*d) + (a*d + b*c)*i>"
msgstr ""
#. type: TP
#: archlinux debian-bookworm debian-unstable fedora-40 fedora-rawhide
#: mageia-cauldron opensuse-leap-15-6 opensuse-tumbleweed
#, no-wrap
msgid "B<division: z/w = ((a*c + b*d)/(c*c + d*d)) + ((b*c - a*d)/(c*c + d*d))*i>"
msgstr ""
#. type: Plain text
#: archlinux debian-bookworm debian-unstable fedora-40 fedora-rawhide
#: mageia-cauldron opensuse-leap-15-6 opensuse-tumbleweed
msgid ""
"Nearly all math function have a complex counterpart but there are some "
"complex-only functions."
msgstr ""
#. type: SH
#: archlinux debian-bookworm debian-unstable fedora-40 fedora-rawhide
#: mageia-cauldron opensuse-leap-15-6 opensuse-tumbleweed
#, no-wrap
msgid "EXAMPLES"
msgstr ""
#. type: Plain text
#: archlinux debian-unstable fedora-40 fedora-rawhide mageia-cauldron
#: opensuse-tumbleweed
msgid ""
"Your C-compiler can work with complex numbers if it supports the C99 "
"standard. The imaginary unit is represented by I."
msgstr ""
#. type: Plain text
#: archlinux debian-unstable fedora-40 fedora-rawhide mageia-cauldron
#: opensuse-tumbleweed
#, no-wrap
msgid ""
"/* check that exp(i * pi) == -1 */\n"
"#include E<lt>math.hE<gt> /* for atan */\n"
"#include E<lt>stdio.hE<gt>\n"
"#include E<lt>complex.hE<gt>\n"
"\\&\n"
"int\n"
"main(void)\n"
"{\n"
" double pi = 4 * atan(1.0);\n"
" double complex z = cexp(I * pi);\n"
" printf(\"%f + %f * i\\en\", creal(z), cimag(z));\n"
"}\n"
msgstr ""
#. type: SH
#: archlinux debian-bookworm debian-unstable fedora-40 fedora-rawhide
#: mageia-cauldron opensuse-leap-15-6 opensuse-tumbleweed
#, no-wrap
msgid "SEE ALSO"
msgstr ""
#. type: Plain text
#: archlinux debian-bookworm debian-unstable fedora-40 fedora-rawhide
#: mageia-cauldron opensuse-leap-15-6 opensuse-tumbleweed
msgid ""
"B<cabs>(3), B<cacos>(3), B<cacosh>(3), B<carg>(3), B<casin>(3), "
"B<casinh>(3), B<catan>(3), B<catanh>(3), B<ccos>(3), B<ccosh>(3), "
"B<cerf>(3), B<cexp>(3), B<cexp2>(3), B<cimag>(3), B<clog>(3), B<clog10>(3), "
"B<clog2>(3), B<conj>(3), B<cpow>(3), B<cproj>(3), B<creal>(3), B<csin>(3), "
"B<csinh>(3), B<csqrt>(3), B<ctan>(3), B<ctanh>(3)"
msgstr ""
#. type: TH
#: debian-bookworm opensuse-leap-15-6
#, no-wrap
msgid "2022-10-30"
msgstr ""
#. type: TH
#: debian-bookworm
#, no-wrap
msgid "Linux man-pages 6.03"
msgstr ""
#. type: Plain text
#: debian-bookworm opensuse-leap-15-6
msgid ""
"Your C-compiler can work with complex numbers if it supports the C99 "
"standard. Link with I<-lm>. The imaginary unit is represented by I."
msgstr ""
#. type: Plain text
#: debian-bookworm opensuse-leap-15-6
#, no-wrap
msgid ""
"/* check that exp(i * pi) == -1 */\n"
"#include E<lt>math.hE<gt> /* for atan */\n"
"#include E<lt>stdio.hE<gt>\n"
"#include E<lt>complex.hE<gt>\n"
msgstr ""
#. type: Plain text
#: debian-bookworm opensuse-leap-15-6
#, no-wrap
msgid ""
"int\n"
"main(void)\n"
"{\n"
" double pi = 4 * atan(1.0);\n"
" double complex z = cexp(I * pi);\n"
" printf(\"%f + %f * i\\en\", creal(z), cimag(z));\n"
"}\n"
msgstr ""
#. type: TH
#: fedora-40 fedora-rawhide mageia-cauldron
#, no-wrap
msgid "2023-10-31"
msgstr ""
#. type: TH
#: fedora-40 mageia-cauldron
#, no-wrap
msgid "Linux man-pages 6.06"
msgstr ""
#. type: TH
#: fedora-rawhide
#, no-wrap
msgid "Linux man-pages 6.7"
msgstr ""
#. type: TH
#: opensuse-leap-15-6
#, no-wrap
msgid "Linux man-pages 6.04"
msgstr ""
#. type: TH
#: opensuse-tumbleweed
#, no-wrap
msgid "Linux man-pages (unreleased)"
msgstr ""
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