notacao: z' = conjugado de z.
"The strong connections between the operations of complex numbers and the geometry of the plane enable us to specify certain important geometrical objects by means of complex equations. The most obvious case is that of the circle {z : |z - c| = r} with centre c and radius r >=0. This easily translates to the familiar form of the equation of a circle: if z = x + iy and c = a + ib, then |z-c|=r if and only if |z-c|^2 = r^2, that is, if and only if (x-a)^2 + (y-b)^2 = r^2. *The other form, x^2 + y^2 + 2gx + 2fy + c = 0, of the equation of the circle can be rewritten as zz' + hz + (hz)' + c = 0, where h = g -if. More generally, we have the equation Azz' + Bz + (Bz)' + C = 0, where A(!=0) and C are real, and B is complex. (...)"
Realmente nao consegui entender a equacao geral da circunferencia que ele apresenta
x^2 + y^2 + 2gx + 2fy + c = 0
Expandi |z-h|^2 = r^2 e chego em x^2 + y^2 - 2gx + 2fy + g^2 + f^2 - r^2...
Ele tb nao deveria definir quem é f e g antes de apresentar a equacao?
Obrigado
Niski ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~nicolau/olimp/obm-l.html =========================================================================
