5. ¿Cuál es el módulo del número complejo ω = 1 + √3i/2? Calcula sus potencias ω2 y ω3, y dibuja los tres (ω, ω2 y ω3) en el plano complejo.

Para calcular o módulo do número complexo ω, que é dado por ω = 1 + √3i/2, podemos usar a fórmula do módulo de um número complexo, que é a raiz quadrada da soma dos quadrados das partes real e imaginária. Primeiro, vamos calcular o módulo de ω: |módulo de ω| = √(parte real)^2 + (parte imaginária)^2 = √(1)^2 + (√3/2)^2 = √1 + 3/4 = √4/4 + 3/4 = √7/4 = √7/2 Agora, vamos calcular ω²: ω² = (1 + √3i/2)² = (1 + √3i/2)(1 + √3i/2) = 1 + √3i/2 + √3i/2 + (√3i/2)² = 1 + √3i/2 + √3i/2 + 3i²/4 = 1 + √3i + √3i - 3/4 = 1 + 2√3i - 3/4 = 1 - 3/4 + 2√3i = 1/4 + 2√3i Por fim, vamos calcular ω³: ω³ = (1 + √3i/2)³ = (1 + √3i/2)(1 + √3i/2)(1 + √3i/2) = (1 + √3i/2)(1 + √3i/2) + √3i/2(1 + √3i/2) + (1 + √3i/2)√3i/2 = (1 + √3i/2 + √3i/2 + (√3i/2)²) + √3i/2 + (√3i/2)² + √3i/2 + (√3i/2)² = 1 + √3i + √3i + 3i/4 + √3i/2 + 3i/4 + √3i/2 + 3i/4 = 1 + 2√3i + 3i/2 + √3i + 3i/2 + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √3i + 3i + √3i + 3i/4 = 1 + 2√3i + 3i + √