bonjour on me demande de resoudre dans lensemble des complexes les deux équations suivantes 1° (1+3I)z+2-4i=0 2° Zau carre+2Z+5=0 MERCI

Bonjour,
1)
(1+3i)z+2-4i = 0 ⇒ (1+3i)z = -2+4i ⇒ z = (-2+4i) / (1+3i) ⇒
z = (-2+4i)(1-3i) / (1-9i²) = (-2+6i+4i-12i²)/10 = (-2+10i+12) / 10 = (10+10i)/10 ⇒
z = 1+i
2)
z²+2z+5 = 0
Δ = 4-20 = -16 = 16i² ⇒ √Δ = 4i
z = (-2-4i)/2 = -1-2i ou z = (-2+4i)/2 = -1+2i