Question

Escreva o número complexo [(1/2)+ raiz 3/2]^2 na forma polar.

Answer 1

Forma polar: $z=|z|.(cos\theta+i.sen\theta)$

Módulo de um complexo: $|z|=\sqrt{a^2+b^2}$

Resposta:

$|z|=\sqrt{(\frac{1}{2})^2+(\frac{\sqrt3}{2})^2}\\|z|=\sqrt{\frac{1}{4}+\frac{3}{4}}\\|z|=\sqrt{1}=1$         $\theta=arctan(\frac{\frac{\sqrt3}{2}}{\frac{1}{2}})\\\theta=arctan(\sqrt3)\\\theta=\frac{\pi}{3}$

$z=|z|.(cos\theta+i.sen\theta)\\z=1.(cos60\°+i.sen60\°)\\z=\frac{1}{2}+i.\frac{\sqrt3}{2}\\z=\frac{1+\sqrt3}{2}i$