Lieu géométrique et nombres complexes (3)

Énoncé

Déterminer les ensembles de points \(\text M(z)\) vérifiant chacune des conditions suivantes.

1. \(\mathscr{E}_1=\left\lbrace \text M(z) \colon \left\vert z-4+3i \right\vert =2 \right\rbrace\)

2. \(\mathscr{E}_2=\left\lbrace \text M(z) \colon \left\vert \dfrac{z+5-2i}{z-3+i} \right\vert = 1 \right\rbrace\)

3. \(\mathscr{E}_3=\left\lbrace \text M(z) \colon \arg\left(\dfrac{z-3-2i}{1+i}\right) \equiv \dfrac{\pi}{2} \ [2\pi] \right\rbrace\)

4. \(\mathscr{E}_4=\left\lbrace \text M(z) \colon \arg\left(\dfrac{z-4i-1}{z-3}\right) \equiv \dfrac{\pi}{2} \ [\pi] \right\rbrace\)

5.  \(\mathscr{E}_5=\left\lbrace \text M(z) \colon \arg\left(\dfrac{z+2-i}{z-1+4i}\right) \equiv \pi \ [2\pi] \right\rbrace\)

6. \(\mathscr{E}_6=\left\lbrace \text M(z) \colon \arg\left(\dfrac{z-1}{z+1}\right) \equiv -\dfrac{\pi}{2} \ [2\pi] \right\rbrace\)