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% ########################### MES PARAMETRES ##############################################################
\def\monnumero{ 4 }
\def\madate{ Janvier 2026}
% ########################### MES PARAMETRES ##############################################################

% en-tête
\lhead{\footnotesize{\textsf{Lycée Schuman Perret\\ \madate}}} %gauche
\chead{\textsf{\textcolor{red}{\textbf{\textsc{SERIE D'EXERCICES \monnumero}}}}} %centre
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%pied de page
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\lfoot{\scriptsize{\textsf{\textsc{Stéphane Le Méteil }}}}

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\begin{document}
%\everymath{\displaystyle}
\doublespacing

\exo Calculer le module des complexes suivants :

\begin{multicols}{3}

\z 1+i.

\z 1-i.

\z -1+i.

\z -1-i.

\z \sqrt{3}-i.

\z \sqrt{2}+5\sqrt{2}i.

\z \dfrac{1}{3-2i}.

\z \dfrac{3}{4+i}.

\z \dfrac{1-2i}{1+3i}.

\z (3-2i)^2.

\z R+jL\omega.

\z \dfrac{R}{R+\frac{1}{jC\omega}}.

\end{multicols}


\setcounter{nz}{0}

\exo Déterminer un argument des complexes suivants :

\begin{multicols}{3}

\z 1+i.

\z 1-i.

\z -1+i.

\z -1-i.

\z -\sqrt{3}+i.

\z 3\sqrt{2}-3i\sqrt{2}.

\z \dfrac{1}{1+i}.

\z \dfrac{3}{-1+i}.

\z \dfrac{3-3i}{\sqrt{3}+i}.

\z \left(\dfrac{\sqrt{6}+i\sqrt{2}}{1-i}\right)^3.


\end{multicols}

\setcounter{nz}{0}

\exo Déterminer l'ensemble de points $M$ d'affixes $z$ tels que :

\begin{multicols}{2}

\begin{enumerate}[a)]
  \item $|z| = 5$
  \item $|z-3| = 1$
  \item $|z+2| = \frac12$
  \item $|2z+3i| = 1$
  \item $|z-4| = |z+4i|$
  \item Re$(z) = 3$
  \item Im$(z) =2$
  \item arg$(z) = \frac{\pi}{3}$
  \item arg$(z-2i) = \frac{\pi}{4}$
\end{enumerate}

\end{multicols}


\end{document}
