Testez vos connaissances sur les nombres complexes !

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[{"id":41756,"question":"Quel est le module du 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 se calcule par |z| = √(a² + b²) = √(3² + (-4)²) = √(9 + 16) = √25 = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41757,"question":"L'argument d'un nombre complexe est toujours mesuré en degrés.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'argument peut être exprimé en degrés ou en radians, selon le contexte.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41758,"question":"La forme trigonométrique d'un nombre complexe z = a + ib est :","option_a":"z = r(cosθ + i sinθ)","option_b":"z = r + iθ","option_c":"z = a cosθ + i b sinθ","option_d":"z = r e^(iθ)","option_e":"","option_f":"","bonne_reponse":"A","explication":"La forme trigonométrique standard est z = r(cosθ + i sinθ), où r est le module et θ l'argument.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41759,"question":"Quel est le conjugué du nombre complexe z = 2 + 3i ?","option_a":"2 - 3i","option_b":"3 + 2i","option_c":"-2 + 3i","option_d":"-2 - 3i","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le conjugué d'un nombre complexe z = a + ib est noté z̄ = a - ib.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41760,"question":"L'équation z² = -1 a pour solution dans ℂ :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les solutions sont z = i et z = -i, qui sont des nombres complexes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41761,"question":"La forme exponentielle d'un nombre complexe z = r(cosθ + i sinθ) est :","option_a":"z = r e^(iθ)","option_b":"z = r e^(-iθ)","option_c":"z = e^(rθ)","option_d":"z = r + e^(iθ)","option_e":"","option_f":"","bonne_reponse":"A","explication":"La formule d'Euler donne z = r e^(iθ) = r(cosθ + i sinθ).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41762,"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":"-3π\/4","option_e":"","option_f":"","bonne_reponse":"D","explication":"L'argument principal est l'angle θ tel que -π \u003C θ ≤ π. Pour z = -1 - i, θ = -3π\/4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41763,"question":"Le produit de deux nombres complexes conjugués est toujours réel.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Si z = a + ib, alors z * z̄ = (a + ib)(a - ib) = a² + b², qui est un nombre réel.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41764,"question":"La racine carrée d'un nombre complexe z = a + ib (avec a \u003C 0 et b = 0) est :","option_a":"√|a| i","option_b":"-√|a| i","option_c":"√a i","option_d":"√a","option_e":"","option_f":"","bonne_reponse":"A","explication":"Si z = -k (k \u003E 0), alors √z = √k i ou √z = -√k i.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41765,"question":"Quel est l'affixe du point M(2, -3) dans le plan complexe ?","option_a":"2 - 3i","option_b":"3 - 2i","option_c":"-2 + 3i","option_d":"2 + 3i","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'affixe d'un point M(x, y) est le nombre complexe z = x + iy.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]