Question

ATIVIDADE 4
Dados os complexos a seguir, represente-os no plano complexo.
a) Zn = 3 + 3i
b) Z₂ = -3 + 3i​

Answer 1

Resposta:

Leia abaixo

Explicação passo-a-passo:

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

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

$\sin \Theta = \dfrac{a}{\rho} = \dfrac{3}{3\sqrt{2}} = \dfrac{\sqrt{2}}{2}$

$\cos \Theta = \dfrac{b}{\rho} = \dfrac{3}{3\sqrt{2}} = \dfrac{\sqrt{2}}{2}$

$\Theta = 45\textdegree = \dfrac{\pi}{4}$

$z = \rho \: cis \: \theta$

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

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

$\rho = \sqrt{(-3)^2 + 3^2} = \sqrt{18} = 3\sqrt{2}$

$\sin \Theta = \dfrac{a}{\rho} = \dfrac{-3}{3\sqrt{2}} = -\dfrac{\sqrt{2}}{2}$

$\cos \Theta = \dfrac{b}{\rho} = \dfrac{3}{3\sqrt{2}} = \dfrac{\sqrt{2}}{2}$

$\Theta = 315\textdegree = \dfrac{7\pi}{4}$

$z = \rho \: cis \: \theta$

$\boxed{\boxed{z = 3\sqrt{2}\:( cos \:\dfrac{7\pi }{4} + i\sin \dfrac{7\pi }{4})}}$