Bonjour Needhelpsvp
Résoudre l'équation suivante :
[tex]iz-5\overline{z}=11-7i\\\\Soit\ z=x+iy\\\\alors\ \ i(x+iy)-5(x-iy)=11-7i\\\\ix-y-5x+5iy=11-7i\\\\ix-y-5x+5iy-11+7i=0\\\\(-5x-y-11)+i(x+5y+7)=0\\\\\\\left\{\begin{matrix}-5x-y-11=0\\x+5y+7=0 \end{matrix}\right.\ \ \ \ \left\{\begin{matrix}-5x-y-11=0\\5(x+5y+7)=0 \end{matrix}\right.\ \ \ \ \left\{\begin{matrix}-5x-y-11=0\\5x+25y+35=0 \end{matrix}\right.[/tex]
Additionnons les équations membre à membre.
[tex]\left\{\begin{matrix}(-5x-y-11)+(5x+25y+35)=0+0\\5x+25y+35=0 \end{matrix}\right.\\\\\\\left\{\begin{matrix}-5x-y-11+5x+25y+35=0\\5x+25y+35=0 \end{matrix}\right\\\\\\\left\{\begin{matrix}24y+24=0\\5x+25y+35=0 \end{matrix}\right.\\\\\\\left\{\begin{matrix}24y=-24\\5x+25y+35=0 \end{matrix}\right.\\\\\\\left\{\begin{matrix}y=-1\\5x+25y+35=0 \end{matrix}\right.[/tex]
[tex]\\\\\\\left\{\begin{matrix}y=-1\\5x+25\times(-1)+35=0 \end{matrix}\right.\ \ \ \ \left\{\begin{matrix}y=-1\\5x-25+35=0 \end{matrix}\right.\ \ \ \ \left\{\begin{matrix}y=-1\\5x+10=0 \end{matrix}\right.\\\\\\\left\{\begin{matrix}y=-1\\5x=-10 \end{matrix}\right.\ \ \ \ \boxed{\left\{\begin{matrix}y=-1\\x=-2 \end{matrix}\right.}[/tex]
Par conséquent, la solution de l'équation est [tex]\boxed{z=-2-i}[/tex]
