Réponse:
[tex] \frac{x + iy - 4}{x + iy + 4} = \frac{x - 4 + iy}{x + 4 + iy} \times \frac{x + 4 - iy}{x + 4 - iy} \\ \\ \frac{x + iy - 4}{x + iy + 4} = \frac{ {x}^{2} - {(4 - iy)}^{2} }{(x + 4 )^{2} + {y}^{2} } \\ \\ \frac{x + iy - 4}{x + iy + 4} = \frac{ {x}^{2} - {(16 - 8iy - {y}^{2} )}}{(x + 4 )^{2} + {y}^{2} } \\ \\ \frac{x + iy - 4}{x + iy + 4} = \frac{ {x}^{2} + {y}^{2} - 16 + 8iy}{(x + 4 )^{2} + {y}^{2} } \\ \\ [/tex]
[tex]Re(Z) = \frac{ {x}^{2} + {y}^{2} - 16}{ {(x + 4)}^{2} + {y}^{2} }
\\ \\ Im(Z) = \frac{8y}{{(x + 4)}^{2} + {y}^{2}} [/tex]