Quiz — 66e44f3f5864a_COURS complexes.pdf

Question 1 sur 5 10:00

[{"id":68,"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},{"id":69,"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},{"id":70,"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},{"id":71,"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},{"id":72,"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}]