Question

expresse a forma trigonometrica de -1+i

Answer 1

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

$\Large\boxed{\begin{array}{l}\sf Z=-1+i\\\sf \rho=\sqrt{(-1)^2+1^2}=\sqrt{1+1}=\sqrt{2}\\\sf cos(\theta)=\dfrac{-1}{\sqrt{2}}=-\dfrac{\sqrt{2}}{2}\\\\\sf sen(\theta)=\dfrac{1}{\sqrt{2}}=\dfrac{\sqrt{2}}{2}\\\\\sf \theta=\dfrac{3\pi}{4}\\\\\sf Z=\sqrt{2}\bigg[cos\bigg(\dfrac{3\pi}{4}\bigg)+i~sen\bigg(\dfrac{3\pi}{4}\bigg)\bigg]\end{array}}$