Question

Passe para a forma trigonométrica os seguintes números complexos: a) -7-7i

Answer 1

$z=a+bi \\ |z|=\sqrt{a^2+b^2} \\ \cos{\theta}=\frac{a}{|z|} \\ \sin{\theta}=\frac{b}{|z|} \\ z=|z|(\cos{\theta}+i \sin{\theta})$

Para $z=-7-7i$ temos:
$z=a+bi \\ |z|=\sqrt{(-7)^2+(-7)^2}=7\sqrt{2} \\ \cos{\theta}=\frac{-7}{7\sqrt{2}}=-\frac{\sqrt{2}}{2} \\ \sin{\theta}=\frac{-7}{7\sqrt{2}}=-\frac{\sqrt{2}}{2} \\ \theta=225^0 \ ou \ 5\pi/4 \\ z=7\sqrt{2}(\cos{225^0}+i \sin{225^0)$