Quiz — 66e44f3f5864a_COURS complexes.pdf

Question 1 sur 5 10:00

[{"id":59859,"question":"Quel est le résultat de (3 + 2i) + (1 - 4i) ?","option_a":"4 - 2i","option_b":"4 + 6i","option_c":"2 - 6i","option_d":"3 - 2i","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'addition de deux nombres complexes s'effectue en additionnant leurs parties réelles et leurs parties imaginaires séparément : (3 + 1) + (2i - 4i) = 4 - 2i.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"4 - 2i\", \"b\": \"4 + 6i\", \"c\": \"2 - 6i\", \"d\": \"3 - 2i\"}}","_debug_options_count":4},{"id":59860,"question":"Si z = 2 - 3i, quel est son conjugué ?","option_a":"-2 + 3i","option_b":"2 + 3i","option_c":"-2 - 3i","option_d":"3 - 2i","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le conjugué d'un nombre complexe z = a + bi est donné par z̄ = a - bi. Ici, z̄ = 2 + 3i.","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 + 3i\", \"b\": \"2 + 3i\", \"c\": \"-2 - 3i\", \"d\": \"3 - 2i\"}}","_debug_options_count":4},{"id":59861,"question":"Quel est le module du nombre complexe z = -1 + i√3 ?","option_a":"2","option_b":"√2","option_c":"√3","option_d":"4","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le module est calculé par |z| = √(a² + b²) = √((-1)² + (√3)²) = √(1 + 3) = √4 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"2\", \"b\": \"√2\", \"c\": \"√3\", \"d\": \"4\"}}","_debug_options_count":4},{"id":59862,"question":"Quelle est la solution de l'équation z² + 4z + 13 = 0 dans l'ensemble des complexes ?","option_a":"z = -2 ± 3i","option_b":"z = 2 ± 3i","option_c":"z = -2 ± i","option_d":"z = 2 ± i","option_e":"","option_f":"","bonne_reponse":"a","explication":"En utilisant la formule des racines d'une équation du second degré, Δ = 16 - 52 = -36, donc z = (-4 ± √(-36))\/2 = (-4 ± 6i)\/2 = -2 ± 3i.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"z = -2 ± 3i\", \"b\": \"z = 2 ± 3i\", \"c\": \"z = -2 ± i\", \"d\": \"z = ","_debug_options_count":4},{"id":59863,"question":"Dans le plan complexe, quel point correspond au nombre complexe z = 3 - 4i ?","option_a":"(3, 4)","option_b":"(-3, 4)","option_c":"(3, -4)","option_d":"(4, -3)","option_e":"","option_f":"","bonne_reponse":"c","explication":"Un nombre complexe z = a + bi correspond au point de coordonnées (a, b) dans le plan complexe. Ici, z = 3 - 4i correspond au point (3, -4).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"(3, 4)\", \"b\": \"(-3, 4)\", \"c\": \"(3, -4)\", \"d\": \"(4, -3)\"}}","_debug_options_count":4}]