Réponse :
Explications étape par étape
z₁ = (1-i)² / (2+i)²
= (1 - 2i - 1 ) / (4 + 4i - 1)
= -2i / 3 +4i
= -2i / 3 +4i * (3-4i) / (3-4i)
= -6i-8 / 9 +16 = -8/25 - 6/25 i
z₂ = (3-2i) (3-4i) /(3+4i) (3-4i)
= (9-12i-6i-8) / (9+16)
= 1/25 - 18/25i
z₃ calculons d'abord: (1-i / 2+i)²
(1-i)/(2+i) * (1-i) / (2+i)
= (1-i-i-1) / (4+2i+2i-1)
= -2i / 3 +4i
= -2i / 3 +4i * (3-4i) / (3-4i)
= -6i-8 / 9+16
= -8/25 - 6/25 i
deuxième membre:
3-2i/3+4i * 3-4i/3-4i
= (9-12i-6i-8) / 9+16
= 1/25 - 18/25i
-8/25 - 6i/25 - ( 1/25 - 18/25i )
= -8/25 - 6i/25 - 1/25 + 18/25i
= -9/25 + 12/25 i
