Question

Calcule o argumento do número complexo Z :
Z = 3 - 6i

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm M\acute odulo~de~um~n\acute umero~complexo}\\\sf \rho=\sqrt{a^2+b^2}\\\underline{\rm Argumento~de~um~n\acute umero~complexo}\\\sf \acute e~o~\hat angulo~\theta~tal~que\\\sf cos(\theta)=\dfrac{a}{\rho}~~e~sen(\theta)=\dfrac{b}{\rho}\end{array}}$

$\Large\boxed{\begin{array}{l}\sf Z=3-6i\\\underline{\rm C\acute alculo~do~m\acute odulo:}\\\sf \rho=\sqrt{3^2+(-6)^2}\\\sf \rho=\sqrt{9+36}\\\sf \rho=\sqrt{45}\\\sf \rho=\sqrt{3^2\cdot5}\\\sf \rho=3\sqrt{5}\\\underline{\rm C\acute alculo~do~argumento}\\\sf cos(\theta)=\dfrac{\backslash\!\!\!3}{\backslash\!\!\!3\sqrt{5}}=\dfrac{\sqrt{5}}{5}\\\\\sf sen(\theta)=\dfrac{-\backslash\!\!\!6}{\backslash\!\!\!3\sqrt{5}}=-\dfrac{2\sqrt{5}}{5}\\\\\sf \theta\approxeq295,57^\circ\end{array}}$