JAMET

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2 years, 297 days

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restart; with(plots):with(LinearAlgebra):unprotect(O); alias(conj = conjugate); conj z = lambda*v+a; La droite D est représentée par son équation complexe Appelons H l'affixe h le pied de la perpendicukaire abaissée de O sur (D) Les vecteurs OH et V sont orthogonaux donc z = lambda v + a h*conj(v)+conj(h)*v = 0; Le point H appartient à la droite (D) donc : h = lambda*v+a; conj(h) = conj(a)+lambda*conj(v); (lambda*v+a)*conj(v)+(conj(a)+lambda*conj(v))*v = 0; solve(%, lambda); h := simplify(subs(lambda = %, lambda*v+a)); a := 3-I*4; v := -2/3+4*I; evalc(h); H := [Re(h), Im(h)]; Représentation graphique d'un cas particulier : f := proc (x) options operator, arrow; -3*x+5 end proc: a := 3: A := [a, f(a)]:O:=[0,0]: zo := [8/3+I*f(8/3)]; ze := [2+I^(eval(diff(f(x), x), x = 2))]; Zo := [8/3, f(8/3)]; Ze := [2, f(2)]; ex := -3*x+5; V := `
conj := conjugate; d := a*x+b*y-c = 0; z := x+I*y; evalc(z+conj(z)); evalc(z-conj(z)); d := expand((1/2)*a*(z+conj(z))+b*(z-conj(z))/(2*I))-c; is(d = z(a-I*b)+conj(z)*(a+I*b)-2*c); varpi = a+I*b; is(d = z*conj(varpi)+conj(z)*varpi-2*c); How to perform calculations correctly ? Thank you.
z1 := a1+I*b1; z2 := a2+I*b2; abs(z1) = 1; abs(z2) = 1; argument(z1) = alpha; argument(z2) = beta; On considère dans ℂ les complexes z1 et z2 de module 1 et d'argument α et β Show that (z1+z2)^2/(z1+z2) est un réel positf ou nul. Dans quel cas est-il nul ? is((z1^2+2*z1*z2+z2^2)/(z1+z2) = z1/z2+z2/z1+2);#wrong answer z1/z2 = exp(I*(alpha-beta)); z2/z1 = exp(I*(beta-alpha)); is(z1/z2+z2/z1+2 = 2*(1+cos(alpha-beta)));#wong answer Miscalculations. Thank you for your help.

Let E all triplets as X=(p,q,r) such as p^2+q^2=r^2. We define the application f of E dans C complex as X in E f(X)=(p+Iq)/r=Z. Calculate abs(Z). Show that in E the law noted * defined by
X1*X2=(p1*p2-q1*q2,p2*q1+p1*q2,r1*r2) is an internal law. Calculate f(X1*X2). Then if X0=(3,4,5), find
X0*X0, X0*(X0*X0).Thank you for the help.

how to show which region of the plan belongs to the argument points between 0 and Pi/2 and the module points between 0 and 2 ?

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