Question

Represente o número complexo z = 1 - i na forma trigonométrica.

Answer 1

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

$\Large\boxed{\begin{array}{l}\sf z=1-i\\\sf\rho=\sqrt{1^2+(-1)^2}\\\sf \rho=\sqrt{1+1}\\\sf \rho=\sqrt{2}\\\sf cos(\theta)=\dfrac{1}{\sqrt{2}}=\dfrac{\sqrt{2}}{2}\\\\\sf sen(\theta)=-\dfrac{1}{\sqrt{2}}=-\dfrac{\sqrt{2}}{2}\\\\\sf\theta=\dfrac{7\pi}{4}\\\large\boxed{\boxed{\boxed{\boxed{\sf Z=\sqrt{2}\bigg[cos\bigg(\dfrac{7\pi}{4}\bigg)+i~sen\bigg(\dfrac{7\pi}{4}\bigg)\bigg]}}}}\end{array}}$