Question

Na figura a seguir, o ponto P é o afixo do número complexo z:

Answer 1

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$\Large\boxed{\sf{\underline{M\acute{o}dulo~de~um~n\acute{u}mero~complexo}}}\\\huge\boxed{\boxed{\boxed{\boxed{{\sf{\rho=\sqrt{a^2+b^2}}}}}}}$

$\Large\boxed{\sf{\underline{Argumento~de~um~n\acute{u}mero~complexo}}}\\\boxed{\tt{\underline{\acute{e}~o~\hat{a}ngulo~\theta~tal~que}}}\\\huge\boxed{\boxed{\boxed{\sf{cos(\theta)~=~\dfrac{a}{\rho}~~~~sen(\theta)=\dfrac{b}{\rho}}}}}$

$\Large\boxed{\sf{\underline{Forma~trigonom\acute{e}trica~de~um~n\acute{u}mero~complexo}}}\\\huge\boxed{\boxed{\boxed{\boxed{\boxed{\sf{z=\rho\left[cos(\theta)+i~sen(\theta)\right]}}}}}}$

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$\sf{z=\sqrt{3}+i}\\\sf{\rho=\sqrt{(\sqrt{3})^2+1^2}}\\\sf{\rho=\sqrt{3+1}=\sqrt{4}=2}\\\sf{cos(\theta)=\dfrac{\sqrt{3}}{2}}\\\sf{sen(\theta)=\dfrac{1}{2}}\\\sf{\theta=30^{\circ}}\\\huge\boxed{\boxed{\boxed{\sf{z=2\cdot\left[cos(30^{\circ})+i~sen(30^{\circ})\right]}}}}\\\huge\boxed{\boxed{\boxed{\boxed{\boxed{\sf{\maltese~alternativa~d}}}}}}$