Question

Forma trigonométrica: A) z= -1 + i

Answer 1

Explicação passo-a-passo:

$z=-1+i$

$|z|=\sqrt{(-1)^2+1^2}$

$|z|=\sqrt{1+1}$

$|z|=\sqrt{2}$

Temos que:

$\text{sen}~\theta=\dfrac{1}{\sqrt{2}}~\longrightarrow~\text{sen}~\theta=\dfrac{\sqrt{2}}{2}$

$\text{cos}~\theta=\dfrac{-1}{\sqrt{2}}~\longrightarrow~\text{cos}~\theta=\dfrac{-\sqrt{2}}{2}$

Assim, $\text{arg}(z)=\dfrac{3\pi}{4}$

Logo:

$z=|z|\cdot(\text{cos}~\theta+i\cdot\text{sen}~\theta)$

$z=\sqrt{2}\cdot\left(\text{cos}~\dfrac{3\pi}{4}+i\cdot\text{sen}~\dfrac{3\pi}{4}\right)$

Answer 2

Resposta: Este é o calculo!