3414 Words14 Pages

Complexe 1
Il n'y a pas de plaisir plus complexe que celui de la pensée. [Jorge Luis Borges]
2012/2013 4 Math
Exercice 1 :Q.C.M. Choisir la ou (les) bonne(s) réponse(s). 1) L’ensemble des points M(z) tels que z=z est : a)une droite b)un cercle, c)une demi droite. 2) L’ensemble des points M(z)tels que z+4=1 est a) vide b) un cercle c) une droite 3) l’ensemble des points M(z) tels que z=z+ z est inclus dans : a)un cercle b) une demi-droite c)deux droites 4) l’ensemble des points M(z) tels quez-i=1-zest : a)vide b) une droite c) un segment 5)l’ensemble des points M(z) ;arg(z+i) = (2) est 2 a) un demi-cercle b) une droite c)une demi-droite _ _ _ 6)Si z = alors a) z = ; b) z = ; c) z = z z z 7)Si z est un nombre complexe non nul d’argument alors un argument de i z est a) ; b) ; 2013 8)Un argument de ( 1+i) est ; ; a) b)-3
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7 4)Donner les valeurs exactes de cos et sin 12 12 Exercice 5 : Déterminer l’ensemble des points M(z) ; tels que : _ a)arg(z-2i) = (2) ;b)arg( z -i) = - (2) ; 4 3 c)arg (z-2i) = arg (-z) (2), f)arg(z-1+i) = arg(- z+1+i) (2) d)z-2i= z +i, e)(z+i)( z -i)=9 g) z= 1-2i + 4(cos + i sin ) où [, ] Exercice 6: Soit z1=1-i ; z2= 1-i 3 et Z = Ecrire sous forme exponentielle les nombres complexes z1, z2 et Z. Déduire les valeurs exactes de cos et sin
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Exercice 7: c) /3 c On pose Z= iz z-1 Déterminer et construire les ensembles suivants E= {M ( Z) tque z=1}; F= {M (z); Z²iIR} Exercice 8: Z étant un nombre complexe IC – IR 3 1°) M (z), B (z²), C (z ) sont trois points distincts. Déterminer l'ensemble des points M du plan pour que le triangle MBC soit rectangle en C. 2°) Déterminer l'ensemble des points M(z) pour que les points A(1), M(z) et M'(1+z2 ) soient alignés Exercice 9: Soit l’application de C* dans C définie par i+z (z) = _ z Exercice 2

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