Question

Encontre as coordenadas polares do ponto P cujas coordenadas
retangulares são $(-2, 2\sqrt{3} )$ .

Answer 1

$\large\boxed{\begin{array}{l}\rm z=-2+2\sqrt{3}i\\\rm r=\sqrt{(-2)^2+(2\sqrt{3})^2}\\\rm r=\sqrt{4+4\cdot3}\\\rm r=\sqrt{4+12}\\\rm r=\sqrt{16}\\\rm r=4\\\begin{cases}\rm cos(\theta)=-\dfrac{2}{4}=-\dfrac{1}{2}\\\\\rm sen(\theta)=\dfrac{\backslash\!\!\!2\sqrt{3}}{\backslash\!\!\!4_2}=\dfrac{\sqrt{3}}{2}\end{cases}\longrightarrow \theta=\dfrac{2\pi}{3}\\\\\rm (r,\theta)=\bigg(4,\dfrac{2\pi}{3}\bigg)\end{array}}$