Question

Determine a forma trigonométrica ou polar do complexo z= -5+5i

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

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

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

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

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

$\mathsf{\rho = \sqrt{50}}$

$\mathsf{\rho = \sqrt{2.5^2}}$

$\mathsf{\rho = 5\sqrt{2}}$

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

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

$\mathsf{\Theta = 135\textdegree = \dfrac{3\pi }{4}}$

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

$\boxed{\boxed{\mathsf{z = 5\sqrt{2}\:(cos\:\dfrac{3\pi }{4} + i\:sen\:\dfrac{3\pi}{4})}}}$