Bonjour,
1) za = 1 + i
za' = 1 + i/za = 1 + i/(1 + i)
= (1 + i + i)/(1 + i)
= (1 + 2i)/(1 + i)
= (1 + 2i)(1 - i)/(1 + i)(1 - i)
= (1 - i + 2i + 2)/2
= (3 + i)/2
donc VRAI
2) z = x + iy
z' = 1 + i/(x + iy)
= (x + iy + i)/(x + iy)
= (x + i(y + 1))(x - iy)/(x + iy)(x - iy)
= (x² - xyi + xyi + y² + xi + y)/(x² + y²)
= (x² + y² + y)/(x² + y²) + xi/(x² + y²)
⇒ Re(z') = VRAI
et Im(z') = FAUX x et non -x
