Question

Se Z= 3+3√3i, represente-o na forma trigonométrica

Answer 1

p=√a²+b²= √(3)²+(3√3)² = √9+27 =√36=6

tgx = b/a = 3√3/3 = √3 ==> x=60°

z = p.(cosx + i.senx)

z = 6.(cos60 + i.sen60) ✓

Answer 2

z = 3 + 3√3i

ρ = √(3)² + (3√3)²

ρ = √9 + 27

ρ = √36 ---> ρ = 6.

Cos Φ = 3/6

Cos Φ = 1/2 ---> Cos 60°

Sen Φ = 3√3/6

Sen Φ = √3/2 ---> Sen 60°

Então temos que:

z = 6(cos 60° + i · sen 60°) ou, z = 6(cos π/3 + i · sen π/3).

Att, Felipemlvr.