Quiz — 1602076088_3-Calcul dans C .pdf

Question 1 sur 5 10:00

[{"id":253,"question":"Quel est le résultat de (3 + 4i) + (2 - 5i) ?","option_a":"5 - i","option_b":"5 + 9i","option_c":"1 - i","option_d":"5 + i","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'addition des nombres complexes se fait en additionnant les parties réelles entre elles et les parties imaginaires entre elles : (3+2) + (4i-5i) = 5 - i.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":254,"question":"Si z = 1 - i√3, quel est son argument principal (en radians) ?","option_a":"π\/3","option_b":"-π\/3","option_c":"2π\/3","option_d":"-2π\/3","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'argument θ d'un nombre complexe z = a + bi est donné par tan(θ) = b\/a. Ici, a=1 et b=-√3, donc θ = arctan(-√3) = -π\/3 (dans l'intervalle ]-π, π]).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":255,"question":"Quelle est la forme trigonométrique de z = -1 + i ?","option_a":"√2(cos(3π\/4) + i sin(3π\/4))","option_b":"√2(cos(π\/4) + i sin(π\/4))","option_c":"2(cos(3π\/4) + i sin(3π\/4))","option_d":"√2(cos(-π\/4) + i sin(-π\/4))","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le module de z est √((-1)² + 1²) = √2. L'argument θ vérifie cos(θ) = -1\/√2 et sin(θ) = 1\/√2, donc θ = 3π\/4. La forme trigonométrique est donc √2(cos(3π\/4) + i sin(3π\/4)).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":256,"question":"Résoudre dans ℂ l'équation z² = -4.","option_a":"z = 2i ou z = -2i","option_b":"z = 2 ou z = -2","option_c":"z = 4i ou z = -4i","option_d":"Pas de solution dans ℂ","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation z² = -4 s'écrit z² = 4i², donc z = ±2i. Les solutions sont donc z = 2i et z = -2i.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":257,"question":"Quel est le conjugué du nombre complexe z = 5 - 3i ?","option_a":"5 + 3i","option_b":"-5 + 3i","option_c":"-5 - 3i","option_d":"3 - 5i","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le conjugué d'un nombre complexe z = a + bi est le nombre complexe de même partie réelle et de partie imaginaire opposée, soit z̄ = a - bi. Ici, z̄ = 5 + 3i.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]