(3-∛3i)⁴ = ?
(3-∛3i)⁴ = (3-∛3i)² * (3-∛3i)² = (9 -6∛3 i +∛9i²)(9 -6∛3 i +∛9i²)=
=(9 -6∛3 i -∛9)*(9 -6∛3 i -∛9)=( (9 - ∛9) -6∛3 i)²=
=(9 - ∛9)² - 2*(9 - ∛9)*6∛3 i + 36∛81 i²=
=81 - 18∛9 + ∛81 -108∛3 i + 12∛27 i - 36∛81=
=81 - 18∛9 + 3∛3 -108∛3 i + 12*3 i - 36*3∛3 =
=81 - 18∛9 - 108∛3 -(108∛3 - 36) i
(3-∛3i)⁴ = ?
(3-∛3i)⁴ = (3-∛3i)² * (3-∛3i)² = (9 -6∛3 i +∛9i²)(9 -6∛3 i +∛9i²)=
=(9 -6∛3 i -∛9)*(9 -6∛3 i -∛9)=( (9 - ∛9) -6∛3 i)²=
=(9 - ∛9)² - 2*(9 - ∛9)*6∛3 i + 36∛81 i²=
=81 - 18∛9 + ∛81 -108∛3 i + 12∛27 i - 36∛81=
=81 - 18∛9 + 3∛3 -108∛3 i + 12*3 i - 36*3∛3 =
=81 - 18∛9 - 108∛3 -(108∛3 - 36) i