{[Aplusix {[modele aplusix_modele] [noms_prop (objet statut_aplusix sorte_activite_aplusix titre_aplusix auteurs_aplusix description_aplusix discipline_aplusix theme_aplusix niveau_aplusix age_aplusix mots_cles_aplusix domaine_calcul domaine_bouton_calcul niv_alg_dyn nombre_maxi_exercices exercices_aleatoires les_langues langage_repertoire lexique_multilingue commentaires_widget nombre_phases_aplusix)] [objet Aplusix] [titre_aplusix "C2 - Quadratic equations on complex numbers, with complex coefficients " ] [auteurs_aplusix "JF Nicaud " ] [description_aplusix "Examples : " (-4ix+2)^[2]+(-4ix+2)(x+2ix-1+i)=0 " " "Automatic calculations using the conjuguate. " ] [discipline_aplusix " " ] [theme_aplusix "Complexes " ] [niveau_aplusix " " ] [age_aplusix " " ] [mots_cles_aplusix " " ] [langue_aplusix " " ] [nombre_phases_aplusix 5] [phases (Aplusix_Phase1 Aplusix_Phase2 Aplusix_Phase3 Aplusix_Phase4 Aplusix_Phase5)] [nombre_maxi_exercices " " ] [exercices_aleatoires non] [domaine_calcul nombres_complexes] [domaine_bouton_calcul calculs_9] [lexique_multilingue " " ] [commentaires_widget " " ] [les_langues " " ] [langage_repertoire "fr " ] [statut_aplusix 2] [niv_alg_dyn 2] [sorte_activite_aplusix libre]}] [Aplusix_Phase1 {[modele aplusix_phase_modele] [noms_prop (objet numero_phase nombre_maxi_exercices exercices_aleatoires type_exercice consigne_exercice commentaires_phase reserve_aplusix exercices_aplusix)] [objet Aplusix_Phase1] [numero_phase 1] [titre_phase " " ] [explication_phase " " ] [nombre_maxi_exercices "1 " ] [exercices_aleatoires oui] [type_exercice operator_solve] [consigne_exercice " " ] [reserve_aplusix {for (ax+bi)(cx+ix+d)+(ax+bi)(ux-c+i)=0 {and {natAnd -4<=a<=4 -4<=b<=4} {natAnd 1<=c<=4 1<=d<=4} [1<=u<=4] [abcdu<>0] {number 10}}} " " ] [exercices_aplusix " " (-x-4i)(4x+ix+1)+(-x-4i)(2x-4+i)=0 " " (3x-3i)(x+ix+1)+(3x-3i)(x-1+i)=0 " " (x-4i)(2x+ix+2)+(x-4i)(2x-2+i)=0 " " (-4x+3i)(3x+ix+2)+(-4x+3i)(4x-3+i)=0 " " (3x+3i)(3x+ix+3)+(3x+3i)(4x-3+i)=0 " " (-x-2i)(2x+ix+1)+(-x-2i)(2x-2+i)=0 " " (x-3i)(2x+ix+4)+(x-3i)(x-2+i)=0 " " (x-i)(4x+ix+3)+(x-i)(4x-4+i)=0 " " (2x+i)(3x+ix+2)+(2x+i)(x-3+i)=0 " " (-2x+i)(2x+ix+2)+(-2x+i)(2x-2+i)=0 " " " " " " ] [liste_exercices ()] [commentaires_phase " " ]}] [Aplusix_Phase2 {[modele aplusix_phase_modele] [noms_prop (objet numero_phase nombre_maxi_exercices exercices_aleatoires type_exercice consigne_exercice commentaires_phase reserve_aplusix exercices_aplusix)] [objet Aplusix_Phase2] [numero_phase 2] [nombre_maxi_exercices "1 " ] [exercices_aleatoires oui] [type_exercice operator_solve] [consigne_exercice " " ] [commentaires_phase " " ] [reserve_aplusix {for az^[2]+biz+c=0 {and [{natAnd -3<=a<=3 {abs [a]}>=1}] [{natAnd -3<=b<=3 {abs [b]}>=1}] [{natAnd -3<=c<=3 {abs [c]}>=1}] [-b^[2]-4ac>0] {number 10}}} " " ] [exercices_aplusix 3z^[2]-3iz-2=0 " " 2z^[2]-3iz-3=0 " " -2z^[2]+2iz+1=0 " " -3z^[2]-iz+1=0 " " 2z^[2]-iz-3=0 " " 2z^[2]+3iz-3=0 " " z^[2]-iz-1=0 " " -3z^[2]-3iz+3=0 " " -3z^[2]-2iz+1=0 " " -z^[2]+iz+1=0 " " " " ] [cibles ()] [liste_exercices ()]}] [Aplusix_Phase3 {[modele aplusix_phase_modele] [noms_prop (objet numero_phase nombre_maxi_exercices exercices_aleatoires type_exercice consigne_exercice commentaires_phase reserve_aplusix exercices_aplusix)] [objet Aplusix_Phase3] [numero_phase 3] [nombre_maxi_exercices "1 " ] [exercices_aleatoires oui] [type_exercice operator_solve] [consigne_exercice " " ] [commentaires_phase " " ] [reserve_aplusix {for (aix+b)^[2]+(aix+b)(ux+dix-c+i)=0 {and {natAnd -4<=a<=4 -4<=b<=4} {natAnd 1<=c<=4 1<=d<=4} [1<=u<=4] [abcdu<>0] {number 10}}} " " ] [exercices_aplusix (4ix-3)^[2]+(4ix-3)(3x+ix-2+i)=0 " " (-2ix-4)^[2]+(-2ix-4)(2x+ix-4+i)=0 " " (4ix-2)^[2]+(4ix-2)(x+2ix-4+i)=0 " " (-4ix+2)^[2]+(-4ix+2)(x+2ix-1+i)=0 " " (3ix+3)^[2]+(3ix+3)(3x+2ix-4+i)=0 " " (-3ix-3)^[2]+(-3ix-3)(4x+4ix-1+i)=0 " " (-3ix-4)^[2]+(-3ix-4)(2x+3ix-2+i)=0 " " (ix+3)^[2]+(ix+3)(x+2ix-3+i)=0 " " (3ix+2)^[2]+(3ix+2)(3x+4ix-3+i)=0 " " (4ix+2)^[2]+(4ix+2)(3x+4ix-1+i)=0 " " " " ] [cibles ()] [liste_exercices ()]}] [Aplusix_Phase4 {[modele aplusix_phase_modele] [noms_prop (objet numero_phase nombre_maxi_exercices exercices_aleatoires type_exercice consigne_exercice commentaires_phase reserve_aplusix exercices_aplusix)] [objet Aplusix_Phase4] [numero_phase 4] [nombre_maxi_exercices "1 " ] [exercices_aleatoires oui] [type_exercice operator_solve] [consigne_exercice " " ] [commentaires_phase " " ] [reserve_aplusix {for aiz^[2]+bz+ci=0 {and [{natAnd -3<=a<=3 {abs [a]}>=1}] [{natAnd -3<=b<=3 {abs [b]}>=1}] [{natAnd -3<=c<=3 {abs [c]}>=1}] [b^[2]+4ac<0] {number 10}}} " " ] [exercices_aplusix iz^[2]+2z-3i=0 " " 3iz^[2]+3z-2i=0 " " 3iz^[2]-3z-3i=0 " " iz^[2]+z-2i=0 " " -3iz^[2]-2z+2i=0 " " -2iz^[2]+z+i=0 " " 2iz^[2]-z-2i=0 " " iz^[2]-2z-3i=0 " " 2iz^[2]-2z-i=0 " " -3iz^[2]+z+2i=0 " " " " ] [liste_exercices ()]}] [Aplusix_Phase5 {[modele aplusix_phase_modele] [noms_prop (objet numero_phase nombre_maxi_exercices exercices_aleatoires type_exercice consigne_exercice commentaires_phase reserve_aplusix exercices_aplusix)] [objet Aplusix_Phase5] [numero_phase 5] [nombre_maxi_exercices "1 " ] [exercices_aleatoires oui] [type_exercice operator_solve] [consigne_exercice " " ] [commentaires_phase " " ] [reserve_aplusix " " {for (aiz+b+di)^[2]=(aiz+c)^[2] {and [{natAnd -4<=a<=4 {abs [a]}>=1}] [{natAnd -4<=b<=4 {abs [b]}>=1}] [{natAnd -4<=c<=4 {abs [c]}>=1}] {natAnd -3<=d<=3 d<>0} {number 10}}} " " ] [exercices_aplusix (iz-3-3i)^[2]=(iz+4)^[2] " " (3iz-2+3i)^[2]=(3iz-3)^[2] " " (3iz+4+3i)^[2]=(3iz-2)^[2] " " (4iz-4-2i)^[2]=(4iz-3)^[2] " " (-2iz+1-2i)^[2]=(-2iz+1)^[2] " " (-3iz+1+i)^[2]=(-3iz-3)^[2] " " (3iz-3-3i)^[2]=(3iz-2)^[2] " " (-2iz-4+i)^[2]=(-2iz-4)^[2] " " (-4iz+4+3i)^[2]=(-4iz-3)^[2] " " (-3iz+4+3i)^[2]=(-3iz+4)^[2] " " ] [liste_exercices ()]}]}