Question

Calcule (3+3i)na forma
polar (trigonométrica).​

Answer 1

Primeiro calculamos o módulo do número z:

\boxed{\rho=\sqrt{3^2+3^2}=\sqrt{18}=3\sqrt{2}}

ρ=

3

2

+3

2

=

18

=3

2

Agora determinando o argumento:

\begin{gathered}\boxed{sen \theta=\frac{3}{3\sqrt2}=\frac{1}{\sqrt2}=\frac{\sqrt2}{2}} \\ \\ \boxed{cos \theta=\frac{3}{3\sqrt2}=\frac{1}{\sqrt2}=\frac{\sqrt2}{2}}\end{gathered}

senθ=

3

2

3

=

2

1

=

2

2

cosθ=

3

2

3

=

2

1

=

2

2

Logo \theta=\frac{\pi}{4}θ=

4

π

assim:

\boxed{z=3\sqrt2(cos \frac{\pi}{4}+i.sen \frac{\pi}{4})}

z=3

2

(cos

4

π

+i.sen

4

π

)