Question

Resolva:
a) (2+3i) ⁴
Números complexos

Answer 1

Lembrar  i = √(-1)

(2+3i)⁴ = (2+3i)² . (2+3i)²

(2+3i)⁴ = (2² + 2 . 2 . 3i + (3i)²) . (2² + 2 . 2 . 3i + (3i)²)

(2+3i)⁴ = (4 + 12i + 3² . i²) . (4 + 12i + 3² . i²)

(2+3i)⁴ = (4 + 12i + 9 . (-1)) . (4 + 12i + 9 . (-1))

(2+3i)⁴ = (4 + 12i - 9) . (4 + 12i - 9)

(2+3i)⁴ = (-5 + 12i) . (-5 + 12i)

(2+3i)⁴ = (-5) . (-5) + (-5) . 12i + 12i . (-5) + 12i . 12i

(2+3i)⁴ = 25 - 60i - 60i + 12² . i²

(2+3i)⁴ = 25 - 120i + 144 . (-1)

(2+3i)⁴ = 25 - 120i - 144

(2+3i)⁴ = -119 - 120i