Question

Determinar a forma trigonométrica e representar no plano de Gauss o número complexo Z= -2 raiz de 3+2i

Answer 1

Z = -2√3 + 2i
ρ² = (-2√3)² +2²
ρ² = 4.3 + 4
ρ² = 16
ρ = 4
cosθ = -a/ρ = -2√3/4= -√3/2
senθ = b/ρ = 2/4 = 1/2          => θ = 150°=> 
150π/180 => θ =5π/6

Z = ρ(cosθ + i.senθ)
Z = 4(cos5π/6 + i.sen5π/6)