Quiz — تمرينين في الأعداد المركبة و التحويلات النقطية مع الحل للتحضيرات النهائية -باك 2018-.pdf

Question 1 sur 10 20:00

[{"id":17529,"question":"Quel est le module d'un nombre complexe z = 3 + 4i ?","option_a":"5","option_b":"7","option_c":"√7","option_d":"√13","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le module d'un nombre complexe z = a + bi est donné par |z| = √(a² + b²). Ici, |3 + 4i| = √(3² + 4²) = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"5\", \"b\": \"7\", \"c\": \"√7\", \"d\": \"√13\"}}","_debug_options_count":4},{"id":17530,"question":"Une rotation de centre O et d'angle θ transforme le point M en M'. Si M a pour affixe z, quelle est l'affixe de M' ?","option_a":"z' = z + θ","option_b":"z' = z * e^(iθ)","option_c":"z' = z \/ e^(iθ)","option_d":"z' = z - θ","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une rotation de centre O et d'angle θ transforme l'affixe z en z' = z * e^(iθ), où e^(iθ) = cosθ + i sinθ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"z' = z + θ\", \"b\": \"z' = z * e^(iθ)\", \"c\": \"z' = z \/ e^(iθ)\", \"","_debug_options_count":4},{"id":17531,"question":"Vrai ou Faux ? Le conjugué d'un nombre complexe z = a + bi est z̄ = a - bi.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, le conjugué d'un nombre complexe z = a + bi est z̄ = a - bi.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":17532,"question":"Quelle transformation ponctuelle associe à tout point M son symétrique par rapport à une droite D ?","option_a":"Translation","option_b":"Rotation","option_c":"Réflexion","option_d":"Homothétie","option_e":"","option_f":"","bonne_reponse":"c","explication":"La réflexion (ou symétrie axiale) associe à tout point M son symétrique par rapport à une droite D.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"Translation\", \"b\": \"Rotation\", \"c\": \"Réflexion\", \"d\": \"Homothét","_debug_options_count":4},{"id":17533,"question":"Vrai ou Faux ? L'homothétie de rapport k \u003E 0 et de centre O transforme un vecteur u en un vecteur de même direction et de norme k fois plus grande.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une homothétie de rapport k \u003E 0 et de centre O transforme un vecteur u en un vecteur de même direction et de norme |k| fois plus grande.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":17534,"question":"Quel est l'argument principal du nombre complexe z = -1 + i ?","option_a":"π\/4","option_b":"3π\/4","option_c":"5π\/4","option_d":"7π\/4","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'argument principal de z = -1 + i est l'angle θ tel que cosθ = -1\/√2 et sinθ = 1\/√2, soit θ = 3π\/4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"π\/4\", \"b\": \"3π\/4\", \"c\": \"5π\/4\", \"d\": \"7π\/4\"}}","_debug_options_count":4},{"id":17535,"question":"Vrai ou Faux ? La composition de deux rotations est toujours une rotation.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La composition de deux rotations est une rotation si la somme des angles est différente de 0 modulo 2π, sinon c'est une translation.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":17536,"question":"Quelle est la forme trigonométrique du nombre complexe z = 1 - i√3 ?","option_a":"2(cos(π\/3) + i sin(π\/3))","option_b":"2(cos(5π\/3) + i sin(5π\/3))","option_c":"2(cos(π\/6) + i sin(π\/6))","option_d":"2(cos(7π\/6) + i sin(7π\/6))","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le module de z = 1 - i√3 est 2, et son argument est -π\/3 (ou 5π\/3), donc sa forme trigonométrique est 2(cos(5π\/3) + i sin(5π\/3)).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"2(cos(π\/3) + i sin(π\/3))\", \"b\": \"2(cos(5π\/3) + i sin(5π\/3))\",","_debug_options_count":4},{"id":17537,"question":"Quelle transformation ponctuelle conserve les distances et les angles ?","option_a":"Translation","option_b":"Rotation","option_c":"Réflexion","option_d":"Homothétie","option_e":"","option_f":"","bonne_reponse":"b","explication":"Les rotations et les translations conservent les distances et les angles, mais seule la rotation conserve aussi les angles orientés.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Translation\", \"b\": \"Rotation\", \"c\": \"Réflexion\", \"d\": \"Homothét","_debug_options_count":4},{"id":17538,"question":"Vrai ou Faux ? Le produit de deux nombres complexes conjugués est toujours un nombre réel.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Si z et z̄ sont conjugués, alors z * z̄ = |z|², qui est toujours un nombre réel positif.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]