{"id":1179,"date":"2015-03-12T11:24:09","date_gmt":"2015-03-12T10:24:09","guid":{"rendered":"http:\/\/www.unimath.fr\/?p=1179"},"modified":"2019-05-04T08:51:06","modified_gmt":"2019-05-04T07:51:06","slug":"dm-guide-nombres-complexes-1","status":"publish","type":"post","link":"http:\/\/www.unimath.fr\/?p=1179","title":{"rendered":"DM guid\u00e9 Nombres complexes n\u00b01"},"content":{"rendered":"

Sujet<\/strong> :\u00a0Cliquer ici<\/a>
\nCorrection en fin de cette page<\/p>\n

    \n
  1. Calcul de l’affixe de C’
    \n[peekaboo_link name=\u00a0\u00bbquestion1″]R\u00e9ponse[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion1″] \\frac{-4}{5}+\\frac{3}{5}i[\/peekaboo_content]
    \nMontrer que C’ appartient au cercle
    \n[peekaboo_link name=\u00a0\u00bbquestion2″]Aide[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion2″]Montrer que OC’ = 1 pour cela calculer le module de\u00a0z_{C}‘[\/peekaboo_content]
    \nMontrer que les points A, C et C’ sont align\u00e9s
    \n[peekaboo_link name=\u00a0\u00bbquestion3″]Aide 1[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion3″] On peut montrer que les vecteurs \\overrightarrow{AC} et\u00a0\\overrightarrow{AC}‘ sont colin\u00e9aires[\/peekaboo_content]
    \n[peekaboo_link name=\u00a0\u00bbquestion3b\u00a0\u00bb]Aide 2[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion3b\u00a0\u00bb]L’affixe de\u00a0\\overrightarrow{AC} est -3+i et l’affixe de\u00a0\\overrightarrow{AC}‘ est\u00a0\\frac{-9}{5}+i\\frac{3}{5}[\/peekaboo_content]<\/li>\n
  2. Points ayant pour image A
    \n[peekaboo_link name=\u00a0\u00bbquestion4″]Aide 1[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion4″]Il faut r\u00e9soudre l’\u00e9quation : z’ = z_{A}[\/peekaboo_content]
    \n[peekaboo_link name=\u00a0\u00bbquestion4b\u00a0\u00bb]Aide 2[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion4b\u00a0\u00bb] Le probl\u00e8me revient \u00e0 r\u00e9soudre\u00a0une \u00e9quation en z et \\overline{z}, pour la r\u00e9soudre on peut poser z=x+iy avec x \u00a0et y r\u00e9els.[\/peekaboo_content]
    \n[peekaboo_link name=\u00a0\u00bbquestion4c\u00a0\u00bb]R\u00e9ponse [\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion4c\u00a0\u00bb]M appartient \u00e0 \\Delta\u00a0si et seulement si x=1\u00a0et donc\u00a0\\Delta est la droite d’\u00e9quation\u00a0x=1[\/peekaboo_content]<\/li>\n
  3. Montrer que M’ appartient au cercle
    \n[peekaboo_link name=\u00a0\u00bbquestion5″]Aide 1[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion5″]Montrer que\u00a0OM’ = 1 en utilisant les propri\u00e9t\u00e9s des modules[\/peekaboo_content]
    \n[peekaboo_link name=\u00a0\u00bbquestion6″]Aide 2[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion6″] \u00a0On pourra utiliser : \\overline{z}-1=\\overline{z-1} d’apr\u00e8s une propri\u00e9t\u00e9 des conjugu\u00e9s[\/peekaboo_content]
    \n[peekaboo_link name=\u00a0\u00bbquestion8″]Aide 3[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion8″] \u00a0On pourra utiliser que le module de\u00a0 \\overline{Z} est \u00e9gal au module de Z pour tout complexe \u00a0Z[\/peekaboo_content]<\/li>\n
  4. Montrer que la fraction est r\u00e9elle.
    \n[peekaboo_link name=\u00a0\u00bbquestion9″]Aide 1[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion9″]La fraction d\u00e9pend de\u00a0z et \\overline{z}, on peut faire appara\u00eetre des r\u00e9els en posant\u00a0z=x+iy avec x \u00a0et y r\u00e9els.[\/peekaboo_content]
    \n[peekaboo_link name=\u00a0\u00bbquestion10″]Aide 2[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion10″] La fraction est r\u00e9elle donc \u00e9gale \u00e0 un r\u00e9el k, ce qui nous am\u00e8ne \u00e0 conclure que des vecteurs sont colin\u00e9aires en reconnaissant des affixes de vecteurs dans la fraction [\/peekaboo_content]<\/li>\n<\/ol>\n

    Correction : <\/span>\u00a0cliquer ici<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

    Sujet :\u00a0Cliquer ici Correction en fin de cette page Calcul de l’affixe de C’ [peekaboo_link name=\u00a0\u00bbquestion1″]R\u00e9ponse[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion1″] [\/peekaboo_content] Montrer que C’ appartient au cercle [peekaboo_link name=\u00a0\u00bbquestion2″]Aide[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion2″]Montrer que OC’ = 1 pour cela calculer le module de\u00a0‘[\/peekaboo_content] Montrer que les points A, C et C’ sont align\u00e9s [peekaboo_link name=\u00a0\u00bbquestion3″]Aide 1[\/peekaboo_link][peekaboo_content name=\u00a0\u00bbquestion3″] On peut montrer que […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"http:\/\/www.unimath.fr\/index.php?rest_route=\/wp\/v2\/posts\/1179"}],"collection":[{"href":"http:\/\/www.unimath.fr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.unimath.fr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.unimath.fr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.unimath.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1179"}],"version-history":[{"count":12,"href":"http:\/\/www.unimath.fr\/index.php?rest_route=\/wp\/v2\/posts\/1179\/revisions"}],"predecessor-version":[{"id":3419,"href":"http:\/\/www.unimath.fr\/index.php?rest_route=\/wp\/v2\/posts\/1179\/revisions\/3419"}],"wp:attachment":[{"href":"http:\/\/www.unimath.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1179"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.unimath.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1179"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.unimath.fr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1179"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}