Question

represente na forma trigonometrica z= -1 - √ 3i

Answer 1

Olá.

Lembre-se de que:

$\boxed{\mathsf{\rho = m\'odulo \: de \: z = \sqrt{a^{2} + b^{2}}}} \\ \\ \\ \boxed{\mathsf{\cos \theta = \dfrac{a}{\rho}}} \\ \\ \\ \boxed{\mathsf{\sin \theta = \dfrac{b}{\rho}}}$

Assim:

$\mathsf{\rho = \sqrt{(-1)^{2} + (- \sqrt{3})^{2}} = \sqrt{4} = 2}}\\ \\ \\ \mathsf{\cos \theta = \dfrac{-1}{2}} \\ \\ \\ \mathsf{\sin \theta = \dfrac{-\sqrt{3}}{2} \rightarrow \theta = \dfrac{4\pi}{3}}$

Na forma polar (ou trigonométrica), temos:


$\boxed{\mathsf{z = \rho (\cos \theta + i \times \sin \theta)}} \\ \\ \\ \mathsf{z = 2 (\cos \dfrac{4\pi}{3} + i \times \sin \dfrac{4\pi}{3})}$

Bons estudos.