Exercice

Dans chacun des nombres complexes suivants donner la partie réelle et la partie imaginaire.

a) \(Z = - 2 - 3i\)
b) \(Z = \frac{{ - 1 + i\sqrt 2 }}{2}\)
c) \(Z = - \sqrt 3 \)
d) \(Z = i\)
e) \(Z = 0\)
f) \(Z = 2 + \frac{i}{{\sqrt 2 }}\)

Correction exercice

Donnons les parties réelles et imaginaires des complexes suivants

a) \(Z = - 2 - \) \(3i \Rightarrow \) \(\left\{ \begin{array}{l}{\mathop{\rm Re}\nolimits} (Z) = - 2\\{\mathop{\rm Im}\nolimits} (Z) = - 3\end{array} \right.\)
b) \(Z = - \frac{1}{2} + \) \(\frac{{i\sqrt 2 }}{2} \Rightarrow \) \(\left\{ \begin{array}{l} {\mathop{\rm Re}\nolimits} (Z) = - \frac{1}{2}\\{\mathop{\rm Im}\nolimits} (Z) = \frac{{\sqrt 2 }}{2}\end{array} \right.\)
c) \(Z = - \sqrt 3 \) \( \Rightarrow \) \(\left\{ \begin{array}{l}{\mathop{\rm Re}\nolimits} (Z) = - \sqrt 3 \\{\mathop{\rm Im}\nolimits} (Z) = 0 \end{array} \right.\)
d) \(Z = i \Rightarrow \) \(\left\{ \begin{array}{l}{\mathop{\rm Re}\nolimits} (Z) = 0\\{\mathop{\rm Im}\nolimits} (Z) = 1\end{array} \right.\)
e) \(Z = 0 \Rightarrow \) \(\left\{ \begin{array}{l}{\mathop{\rm Re}\nolimits} (Z) = 0\\{\mathop{\rm Im}\nolimits} (Z) = 0\end{array} \right.\)
f) \(Z = 2 + \frac{i}{{\sqrt 2 }}\) \( \Rightarrow \left\{ \begin{array}{l}{\mathop{\rm Re}\nolimits} (Z) = 2\\{\mathop{\rm Im}\nolimits} (Z) = \frac{1}{{\sqrt 2 }}\end{array} \right.\)