{"id":157,"date":"2008-04-28T23:38:17","date_gmt":"2008-04-28T21:38:17","guid":{"rendered":"http:\/\/wordpress.callac.online\/index.php\/nombres-complexes-avec-xcas\/"},"modified":"2023-10-14T20:13:58","modified_gmt":"2023-10-14T18:13:58","slug":"nombres-complexes-avec-xcas","status":"publish","type":"page","link":"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/nombres-complexes-avec-xcas\/","title":{"rendered":"Nombres complexes avec Xcas"},"content":{"rendered":"

\nVoici comment on peut r\u00e9soudre un exercice classique sur les nombres complexes.<\/p>\n

Enonc\u00e9<\/h2>\n
\n

Le plan complexe est rapport\u00e9 \u00e0 un rep\u00e8re orthonormal direct $(O~;\\overrightarrowu<\/em>,\\overrightarrowv<\/em>)$. On prendra $1~cm$ pour unit\u00e9 graphique. Les questions suivantes sont ind\u00e9pendantes.<\/p>\n

1) R\u00e9soudre, dans l’ensemble $\\C$ des nombres complexes, l\u00a0\u00bbequation :<\/p>\n

$$ \\overlinez<\/em> – 3\\texti<\/em>z – 3+ 6\\texti<\/em> = 0$$<\/p>\n

o\u00f9 $\\overlinez<\/em>$ est le conjugu\u00e9 de $z$.<\/p>\n

2) On consid\u00e8re le point $A$ d’affixe $4 – 2\\texti<\/em>$.<\/p>\n

D\u00e9terminer la forme alg\u00e9brique de l’affixe du point $B$ tel que $OAB$ soit un triangle \u00e9quilat\u00e9ral de sens direct.<\/p>\n

R\u00e9solution \u00e0 l’aide de Xcas<\/h2>\n
\n

1) R\u00e9soudre, dans l’ensemble $\\C$ des nombres complexes, l\u00a0\u00bbequation :<\/p>\n

$$ \\overlinez<\/em> – 3\\texti<\/em>z – 3+ 6\\texti<\/em> = 0$$<\/p>\n

o\u00f9 $\\overlinez<\/em>$ est le conjugu\u00e9 de $z$.<\/p>\n

\n\ncsolve(conj(z)-3i*z-3+6i=0,z)\n<\/code>\n<\/font color><\/p>\n

$$\\left[\\frac9-6*i<\/em>4-4*i<\/em>\\right]$$<\/p>\n

\n\nsimplifier(csolve(conj(z)-3i*z-3+6i=0,z))\n<\/code>\n<\/font color><\/p>\n

$$\\left[\\frac15<\/em>8<\/em>\\mbox+<\/em>\\frac3*i<\/em>8<\/em>\\right]$$<\/p>\n

2) On consid\u00e8re le point $A$ d’affixe $4 – 2\\texti<\/em>$.<\/p>\n

D\u00e9terminer la forme alg\u00e9brique de l’affixe du point $B$ tel que $OAB$ soit un triangle \u00e9quilat\u00e9ral de sens direct.<\/p>\n

\n\na:=4-2*i\n<\/code>\n<\/font color><\/p>\n

$$4-2*i$$<\/p>\n

\n\nb:=a*exp(i*pi\/3)\n<\/code>\n<\/font color><\/p>\n

$$4-2*i\\cdot (\\frac1<\/em>2<\/em>\\mbox+<\/em>\\fraci\\cdot \\sqrt3<\/strong>2<\/em>)$$<\/p>\n

\n\nsimplifier(re(b))\n<\/code>\n<\/font color><\/p>\n

$$\\sqrt3<\/em>\\mbox+<\/em>2$$<\/p>\n

\n\nsimplifier(im(b))\n<\/code>\n<\/font color><\/p>\n

$$2\\cdot \\sqrt3<\/em>-1$$<\/p>\n

<\/math><\/p>\n","protected":false},"excerpt":{"rendered":"

Voici comment on peut r\u00e9soudre un exercice classique sur les nombres complexes. Enonc\u00e9 Le plan complexe est rapport\u00e9 \u00e0 un rep\u00e8re orthonormal direct $(O~;\\overrightarrowu,\\overrightarrowv)$. On prendra $1~cm$ pour unit\u00e9 graphique.…<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":1637,"menu_order":3,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-157","page","type-page","status-publish","hentry"],"yoast_head":"\nNombres complexes avec Xcas - Maths & Num\u00e9rique<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/nombres-complexes-avec-xcas\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Nombres complexes avec Xcas - Maths & Num\u00e9rique\" \/>\n<meta property=\"og:description\" content=\"Voici comment on peut r\u00e9soudre un exercice classique sur les nombres complexes. Enonc\u00e9 Le plan complexe est rapport\u00e9 \u00e0 un rep\u00e8re orthonormal direct $(O~;overrightarrowu,overrightarrowv)$. On prendra $1~cm$ pour unit\u00e9 graphique.…\" \/>\n<meta property=\"og:url\" content=\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/nombres-complexes-avec-xcas\/\" \/>\n<meta property=\"og:site_name\" content=\"Maths & Num\u00e9rique\" \/>\n<meta property=\"article:modified_time\" content=\"2023-10-14T18:13:58+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/nombres-complexes-avec-xcas\/\",\"url\":\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/nombres-complexes-avec-xcas\/\",\"name\":\"Nombres complexes avec Xcas - Maths & Num\u00e9rique\",\"isPartOf\":{\"@id\":\"https:\/\/wordpress.callac.online\/#website\"},\"datePublished\":\"2008-04-28T21:38:17+00:00\",\"dateModified\":\"2023-10-14T18:13:58+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/nombres-complexes-avec-xcas\/#breadcrumb\"},\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/nombres-complexes-avec-xcas\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/nombres-complexes-avec-xcas\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Accueil\",\"item\":\"https:\/\/wordpress.callac.online\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Logiciels math\u00e9matiques\",\"item\":\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Xcas\",\"item\":\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"Nombres complexes avec Xcas\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/wordpress.callac.online\/#website\",\"url\":\"https:\/\/wordpress.callac.online\/\",\"name\":\"Maths & Num\u00e9rique\",\"description\":\"Des outils pour les enseignants de math\u00e9matiques et de num\u00e9rique\",\"publisher\":{\"@id\":\"https:\/\/wordpress.callac.online\/#\/schema\/person\/04061f1ca2c2c42039142a704be95940\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/wordpress.callac.online\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"fr-FR\"},{\"@type\":[\"Person\",\"Organization\"],\"@id\":\"https:\/\/wordpress.callac.online\/#\/schema\/person\/04061f1ca2c2c42039142a704be95940\",\"name\":\"dlefur\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"fr-FR\",\"@id\":\"https:\/\/wordpress.callac.online\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/4a9e17be136808c6597f28aa2b6c13126dab066fdc2198ff60090972c9b7fafc?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/4a9e17be136808c6597f28aa2b6c13126dab066fdc2198ff60090972c9b7fafc?s=96&d=mm&r=g\",\"caption\":\"dlefur\"},\"logo\":{\"@id\":\"https:\/\/wordpress.callac.online\/#\/schema\/person\/image\/\"},\"description\":\"Enseignant de math\u00e9matiques Lyc\u00e9e Pasteur S\u00e3o Paulo\",\"sameAs\":[\"http:\/\/wordpress.callac.online\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Nombres complexes avec Xcas - Maths & Num\u00e9rique","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/nombres-complexes-avec-xcas\/","og_locale":"fr_FR","og_type":"article","og_title":"Nombres complexes avec Xcas - Maths & Num\u00e9rique","og_description":"Voici comment on peut r\u00e9soudre un exercice classique sur les nombres complexes. 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