@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr:-THPXX327-8
  skos:prefLabel "complex conjugate"@en, "conjugué complexe"@fr ;
  a skos:Concept ;
  skos:broader psr:-PFC2HSVT-Z .

psr:-LFGMM85W-J
  skos:prefLabel "demi-plan de Poincaré"@fr, "Poincaré half-plane model"@en ;
  a skos:Concept ;
  skos:related psr:-PFC2HSVT-Z .

psr:-C416GZ5R-Z
  skos:prefLabel "nombre imaginaire pur"@fr, "imaginary number"@en ;
  a skos:Concept ;
  skos:broader psr:-PFC2HSVT-Z .

psr:-TT0V0XBL-P
  skos:prefLabel "entier quadratique"@fr, "quadratic integer"@en ;
  a skos:Concept ;
  skos:broader psr:-PFC2HSVT-Z .

psr:-QJX0PFSZ-1
  skos:prefLabel "partie réelle"@fr, "real part"@en ;
  a skos:Concept ;
  skos:broader psr:-PFC2HSVT-Z .

psr: a skos:ConceptScheme .
psr:-RC6CZ89C-1
  skos:prefLabel "module d'un nombre complexe"@fr, "modulus of a complex number"@en ;
  a skos:Concept ;
  skos:broader psr:-PFC2HSVT-Z .

psr:-PFC2HSVT-Z
  skos:narrower psr:-C416GZ5R-Z, psr:-TT0V0XBL-P, psr:-QJX0PFSZ-1, psr:-RC6CZ89C-1, psr:-S9P4NRFV-X, psr:-MJZBFMWQ-2, psr:-THPXX327-8 ;
  skos:inScheme psr: ;
  skos:related psr:-X5920MNG-M, psr:-LFGMM85W-J, psr:-HQ5Q6664-2, psr:-TXRS2VPR-R ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Complex_number>, <https://fr.wikipedia.org/wiki/Nombre_complexe> ;
  skos:prefLabel "nombre complexe"@fr, "complex number"@en ;
  a skos:Concept ;
  skos:broader psr:-Z5NBGSJC-F ;
  skos:definition """In mathematics, a <b>complex number</b> is an element of a number system that extends the real numbers with a specific element denoted <span class="texhtml mvar" style="font-style:italic;">i</span>, called the imaginary unit and satisfying the equation <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle i^{2}=-1}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msup>
<br/>          <mi>i</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>2</mn>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mo>=</mo>
<br/>        <mo>−<!-- − --></mo>
<br/>        <mn>1</mn>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle i^{2}=-1}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88e98a401d352e5037d5043028e2d7f449e83fa6" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.505ex; width:7.926ex; height:2.843ex;" alt="{\\\\displaystyle i^{2}=-1}"></span>; every complex number can be expressed in the form <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle a+bi}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>a</mi>
<br/>        <mo>+</mo>
<br/>        <mi>b</mi>
<br/>        <mi>i</mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle a+bi}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a92f853c2c9235c06be640b91b7c75e2a907cbda" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.505ex; width:5.87ex; height:2.343ex;" alt="a + bi"></span>, where <span class="texhtml mvar" style="font-style:italic;">a</span> and <span class="texhtml mvar" style="font-style:italic;">b</span> are real numbers. Because no real number satisfies the above equation, <span class="texhtml mvar" style="font-style:italic;">i</span> was called an imaginary number by René Descartes. For the complex number <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle a+bi}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>a</mi>
<br/>        <mo>+</mo>
<br/>        <mi>b</mi>
<br/>        <mi>i</mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle a+bi}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a92f853c2c9235c06be640b91b7c75e2a907cbda" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.505ex; width:5.87ex; height:2.343ex;" alt="a+bi"></span>, <span class="texhtml mvar" style="font-style:italic;">a</span> is called the <b><style data-mw-deduplicate="TemplateStyles:r1023754711">.mw-parser-output .vanchor>:target~.vanchor-text{background-color:#b1d2ff}</style><span class="vanchor"><span id="real_part"></span><span class="vanchor-text">real part</span></span></b>, and <span class="texhtml mvar" style="font-style:italic;">b</span> is called the <b><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1023754711"><span class="vanchor"><span id="imaginary_part"></span><span class="vanchor-text">imaginary part</span></span></b>. The set of complex numbers is denoted by either of the symbols <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle \\\\mathbb {C} }">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mi mathvariant="double-struck">C</mi>
<br/>        </mrow>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbb {C} }</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9add4085095b9b6d28d045fd9c92c2c09f549a7" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="\\\\mathbb {C} "></span> or <span class="texhtml"><b>C</b></span>. Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers and are fundamental in many aspects of the scientific description of the natural world. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Complex_number">https://en.wikipedia.org/wiki/Complex_number</a>)"""@en, """En mathématiques, l'ensemble des <b>nombres complexes</b> est actuellement défini comme une extension de l'ensemble des nombres réels, contenant en particulier un <i>nombre imaginaire</i> noté <span class="texhtml">i</span>, tel que <span class="texhtml">i<sup>2</sup> = −1</span>. Le carré de <span class="texhtml">(−i)</span> est aussi égal à −1&nbsp;: <span class="texhtml">(−i)<sup>2</sup> = −1</span>. Tout nombre complexe peut s'écrire sous la forme <span class="texhtml"><i>x</i> + i <i>y</i></span> où <span class="texhtml"><i>x</i></span> et <span class="texhtml"><i>y</i></span> sont des nombres réels.
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Nombre_complexe">https://fr.wikipedia.org/wiki/Nombre_complexe</a>)"""@fr ;
  dc:modified "2023-08-17"^^xsd:date .

psr:-S9P4NRFV-X
  skos:prefLabel "imaginary part"@en, "partie imaginaire"@fr ;
  a skos:Concept ;
  skos:broader psr:-PFC2HSVT-Z .

psr:-HQ5Q6664-2
  skos:prefLabel "complex algebraic variety"@en, "variété algébrique complexe"@fr ;
  a skos:Concept ;
  skos:related psr:-PFC2HSVT-Z .

psr:-X5920MNG-M
  skos:prefLabel "complex geometry"@en, "géométrie complexe"@fr ;
  a skos:Concept ;
  skos:related psr:-PFC2HSVT-Z .

psr:-MJZBFMWQ-2
  skos:prefLabel "imaginary unit"@en, "unité imaginaire"@fr ;
  a skos:Concept ;
  skos:broader psr:-PFC2HSVT-Z .

psr:-Z5NBGSJC-F
  skos:prefLabel "nombre"@fr, "number"@en ;
  a skos:Concept ;
  skos:narrower psr:-PFC2HSVT-Z .

psr:-TXRS2VPR-R
  skos:prefLabel "racine de l'unité"@fr, "root of unity"@en ;
  a skos:Concept ;
  skos:related psr:-PFC2HSVT-Z .