Réponse :

Bonjour

Exercice 8

1) j² = = =

2) j² + j + 1 = = -1 + 1 = 0

j³ = j²×j = = = = 1

= = = j² =j barre

Exercice 9

1) 4z + 6 - 2i = 5z - 4 + 2i

⇔ 4z - 5z = -4 + 2i - 6 + 2i

⇔ -z = -10 + 4i

⇔ z = 10 - 4i

2) (5 + 2i)z - 8 = 2 - i

⇔ (5 + 2i)z = 10 - i

⇔ z = (10 - i)/(5 + 2i)

⇔ z = [(10 - i)(5 - 2i)]/[(5 + 2i)(5 - 2i)]

⇔ z = (50 - 20i - 5i + 2i²)/(5² - 4i²)

⇔ z = (46 - 25i)/29

⇔ z =

3) (9 + i)z + 6 - 2i = 5 - (2 + 2i)z + 4

⇔ (9 + i)z + (2 + 2i)z = 5 - 4 + 6 + 2i

⇔ (9 + i + 2 + 2i)z = 7 + 2i

⇔ (11 + 3i)z = 7 + 2i

⇔ z = (7 + 2i)/(11 + 3i)

⇔ z = [(7 + 2i)(11 - 3i)]/[(11 + 3i)(11 - 3i)]

⇔ z = (77 - 21i + 22i - 6i²)/(11² - 9i²)

⇔ z = (83 + i)/130

⇔ z =