Question

01) Calcule z1/z2 sabendo que:

a) √3/2 [ cos π/3 + i sen π/3 ]
b) 2/√3 [ cos π/3 + i sen π/3 ]
c) √3/2 [ cos π/3 - i sen π/3 ]
d) √3/2 [ cos 5π/3 + i sen 5π/3 ]
e) Nenhuma das alternativas.

Answer 1

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$\boxed{\underline{\sf quociente~de~n\acute umeros~complexos~na~forma~trigonom\acute etrica}}\\\large\boxed{\boxed{\boxed{\boxed{\sf\dfrac{z_1}{z_2}=\dfrac{\rho_1}{\rho_2}[cos(\theta_1-\theta_2)+i~sen(\theta_1-\theta_2)]}}}}$

$\sf\dfrac{z_1}{z_2}=\dfrac{2}{\sqrt{3}}\left[cos\left(\dfrac{\pi}{3}-\dfrac{2\pi}{3}\right)+i~sen\left(\dfrac{\pi}{3}-\dfrac{2\pi}{3}\right)\right]\\\sf\dfrac{z_1}{z_2}=\dfrac{2}{\sqrt{3}}\left[cos\left(-\dfrac{\pi}{3}\right)+i~sen\left(-\dfrac{\pi}{3}\right)\right]$

$\sf cos\left(-\dfrac{\pi}{3}\right)=cos\left(\dfrac{\pi}{3}\right)\\\sf sen\left(-\dfrac{\pi}{3}\right)=-sen\left(\dfrac{\pi}{3}\right)\\\large\boxed{\boxed{\boxed{\boxed{\sf\dfrac{z_!}{z_2}=\dfrac{2}{\sqrt{3}}\left[cos\left(\dfrac{\pi}{3}\right)-i~sen\left(\dfrac{\pi}{3}\right)\right]}}}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~e}}}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf Espero~ter~ajudado~^\star~_{\cup}~^\star}}}}$