Question

Escreva os complexos na forma trigonométrica dos complexos: a) z = 1 + i b) a = -1 e b = √3

Answer 1

a) a = 1, b = 1

ρ = √(a² + b²) = √(1² + 1²) = √(1 + 1) = √2

cos θ = a/ρ = 1/√2 = √2/2

sen θ = b/ρ = 1/√2 = √2/2

⇒ θ = 45°

z = ρ cis θ = √2 cis 45°.

b) a = -1, b = √3

ρ = √(a² + b²) = √((-1)² + (√3)²) = √(1 + 3) = √4 = 2

cos θ = a/ρ = -1/2

sen θ = b/ρ = √3/2

⇒ θ = 120°

z = ρ cis θ = 2 cis 120°.