Question

Qual a representação trigonométrica do número complexo abaixo? Z= -5√3+5i

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{z = -5\sqrt{3} + 5i}$

$\mathsf{\rho = \sqrt{a^2 + b^2}}$

$\mathsf{\rho = \sqrt{(-5\sqrt{3})^2 + 5^2}}$

$\mathsf{\rho = \sqrt{75 + 25}}$

$\mathsf{\rho = \sqrt{100}}$

$\mathsf{\rho = 10}$

$\mathsf{cos\:\Theta = \dfrac{a}{\rho} = -\dfrac{5\sqrt{3}}{10} = -\dfrac{\sqrt{3}}{2}}$

$\mathsf{sen\:\Theta = \dfrac{b}{\rho} = \dfrac{5}{10} = \dfrac{1}{2}}$

$\mathsf{\Theta = 150\textdegree = \dfrac{5\pi }{6} }$

$\mathsf{z = \rho\left(cos\:\Theta + i\:sen\:\Theta\right)}$

$\boxed{\boxed{\mathsf{z = 10\left(cos\:\dfrac{5\pi }{6} + i\:sen\:\dfrac{5\pi }{6}\right)}}}$