# German translation of manpages
# This file is distributed under the same license as the manpages-l10n package.
# Copyright © of this file:
# Jens Rohler <jkcr@rohler.de>
# Martin Eberhard Schauer <Martin.E.Schauer@gmx.de>, 2010.
msgid ""
msgstr ""
"Project-Id-Version: manpages-l10n 4.19.0\n"
"POT-Creation-Date: 2024-06-01 05:45+0200\n"
"PO-Revision-Date: 2023-08-11 20:50+0200\n"
"Last-Translator: Martin Eberhard Schauer <Martin.E.Schauer@gmx.de>\n"
"Language-Team: German <debian-l10n-german@lists.debian.org>\n"
"Language: de\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 "complex"

#. type: TH
#: archlinux debian-unstable opensuse-tumbleweed
#, no-wrap
msgid "2024-05-02"
msgstr "2. Mai 2024"

#. type: TH
#: archlinux debian-unstable
#, no-wrap
msgid "Linux man-pages 6.8"
msgstr "Linux man-pages 6.8"

#. type: SH
#: archlinux debian-bookworm debian-unstable fedora-40 fedora-rawhide
#: mageia-cauldron opensuse-leap-15-6 opensuse-tumbleweed
#, no-wrap
msgid "NAME"
msgstr "BEZEICHNUNG"

#. 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 "complex - Grundlagen der komplexen Mathematik"

#. type: SH
#: archlinux debian-unstable fedora-40 fedora-rawhide mageia-cauldron
#: opensuse-tumbleweed
#, no-wrap
msgid "LIBRARY"
msgstr "BIBLIOTHEK"

#. type: Plain text
#: archlinux debian-unstable fedora-40 fedora-rawhide mageia-cauldron
#: opensuse-tumbleweed
msgid "Math library (I<libm>, I<-lm>)"
msgstr "Mathematik-Bibliothek (I<libm>, I<-lm>)"

#. type: SH
#: archlinux debian-bookworm debian-unstable fedora-40 fedora-rawhide
#: mageia-cauldron opensuse-leap-15-6 opensuse-tumbleweed
#, no-wrap
msgid "SYNOPSIS"
msgstr "ÜBERSICHT"

#. 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 "B<#include E<lt>complex.hE<gt>>\n"

#. type: SH
#: archlinux debian-bookworm debian-unstable fedora-40 fedora-rawhide
#: mageia-cauldron opensuse-leap-15-6 opensuse-tumbleweed
#, no-wrap
msgid "DESCRIPTION"
msgstr "BESCHREIBUNG"

#. 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 ""
"Komplexe Zahlen sind Zahlen der Form z = a+b*i, wobei a und b reelle Zahlen "
"sind und i = sqrt(-1), also i*i = -1."

#. 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 ""
"Es gibt andere Darstellungen dieser Zahl. Das Paar (a,b) reeller Zahlen kann "
"als Punkt in der Ebene betrachtet werden, der durch die X- und Y-Koordinaten "
"gegeben ist. Derselbe Punkt kann auch durch ein Paar (r,phi) von reellen "
"Zahlen beschrieben werden, wobei r der Abstand vom Ursprung O ist und phi "
"der Winkel zwischen der X-Achse und der Geraden Oz. Es ist z = r*exp(i*phi) "
"= r*(cos(phi)+i*sin(phi))."

#. 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 ""
"Die grundlegenden Operationen sind auf z = a+b*i und w = c+d*i "
"folgendermaßen definiert:"

#. 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 "B<Addition: z+w = (a+c) + (b+d)*i>"

#. 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 "B<Multiplikation: z*w = (a*c - b*d) + (a*d + b*c)*i>"

#. 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 "B<Division: z/w = ((a*c + b*d)/(c*c + d*d)) + ((b*c - a*d)/(c*c + d*d))*i>"

#. 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 ""
"Nahezu alle Funktionen aus math.h haben komplexe Entsprechungen, aber es "
"gibt auch einige Funktionen, die es nur in complex.h gibt."

#. type: SH
#: archlinux debian-bookworm debian-unstable fedora-40 fedora-rawhide
#: mageia-cauldron opensuse-leap-15-6 opensuse-tumbleweed
#, no-wrap
msgid "EXAMPLES"
msgstr "BEISPIELE"

#. 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 ""
"Ihr C-Compiler kann mit komplexen Zahlen arbeiten, wenn er den C99-Standard "
"unterstützt. Die imaginäre Einheit wird durch I dargestellt."

#. 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 ""
"/* überprüfe exp(i*pi) == -1 */\n"
"#include E<lt>math.hE<gt>        /* für atan */\n"
"#include E<lt>complex.hE<gt>\n"
"#include E<lt>stdio.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"

#. 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 "SIEHE AUCH"

#. 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 ""
"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)"

#. type: TH
#: debian-bookworm opensuse-leap-15-6
#, no-wrap
msgid "2022-10-30"
msgstr "30. Oktober 2022"

#. type: TH
#: debian-bookworm
#, no-wrap
msgid "Linux man-pages 6.03"
msgstr "Linux man-pages 6.03"

#. 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 ""
"Ihr C-Compiler kann mit komplexen Zahlen arbeiten, wenn er den C99-Standard "
"unterstützt. Sie müssen mit I<-lm> linken. Die imaginäre Einheit wird durch "
"I dargestellt."

#. 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 ""
"/* überprüfe exp(i*pi) == -1 */\n"
"#include E<lt>math.hE<gt>        /* für atan */\n"
"#include E<lt>complex.hE<gt>\n"
"#include E<lt>stdio.hE<gt>\n"

#. 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 ""
"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"

#. type: TH
#: fedora-40 fedora-rawhide mageia-cauldron
#, no-wrap
msgid "2023-10-31"
msgstr "31. Oktober 2023"

#. type: TH
#: fedora-40 mageia-cauldron
#, no-wrap
msgid "Linux man-pages 6.06"
msgstr "Linux man-pages 6.06"

#. type: TH
#: fedora-rawhide
#, no-wrap
msgid "Linux man-pages 6.7"
msgstr "Linux man-pages 6.7"

#. type: TH
#: opensuse-leap-15-6
#, no-wrap
msgid "Linux man-pages 6.04"
msgstr "Linux-Handbuchseiten 6.04"

#. type: TH
#: opensuse-tumbleweed
#, no-wrap
msgid "Linux man-pages (unreleased)"
msgstr "Linux man-pages (unveröffentlicht)"