Question

determine a forma trigonométrica de: a) z1= -5 e b) z2= 1 + i√3

Answer 1

Número complexo na forma trigonométrica

$\large\boxed{\boxed{\boxed{\boxed{\mathsf{z=\rho(cos(\theta)+isen(\theta))}}}}}$

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a)

$\mathsf{\rho=\sqrt{(-5)^2}=|-5|=5}\\\mathsf{cos(\theta)=\dfrac{-5}{5}=-1}\\\mathsf{sen(\theta)=\dfrac{0}{5}=0}\\\mathsf{\theta=\pi}\\\large\boxed{\boxed{\boxed{\boxed{\mathsf{z=5\left(cos(\pi)+isen(\pi)\right)}}}}}$

b)

$\mathsf{\rho=\sqrt{1^2+(\sqrt{3})^2}=\sqrt{1+3}=2}\\\mathsf{cos(\theta)=\dfrac{1}{2}}\\\mathsf{sen(\theta)=\dfrac{\sqrt{3}}{2}}\\\mathsf{\theta=\dfrac{\pi}{3}}\\\large\boxed{\boxed{\boxed{\boxed{\mathsf{z=2\left(cos\left(\dfrac{\pi}{3}\right)+isen\left(\dfrac{\pi}{3}\right)\right)}}}}}$

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