Question

Encontre as coordenadas retangulares do ponto P cujas coordenadas polares são $( 6, \frac{2\pi }{3} )$ .

Answer 1

$\large\boxed{\begin{array}{l}\rm z=6\bigg[cos\bigg(\dfrac{2\pi}{3}\bigg)+i~sen\bigg(\dfrac{2\pi}{3}\bigg)\bigg]\\\\\rm z=6\cdot\bigg[-\dfrac{1}{2}+i\cdot\dfrac{\sqrt{3}}{2}\bigg]\\\\\rm z=-3+3\sqrt{3}i\longrightarrow P(-3,3\sqrt{3})\end{array}}$