Question

forma trigonométrica z1 = 4 + 4i em radianos

Answer 1

Forma trigonométrica de um número complexo

$\Large\boxed{\boxed{\boxed{\boxed{\mathsf{z=\rho\cdot\left[cos(\theta)+i\cdot sen(\theta)\right]}}}}}$

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$\mathsf{z_1=4+4i}\\\mathsf{\rho=\sqrt{4^2+4^2}=\sqrt{2\cdot4^2}=4\sqrt{2}}\\\mathsf{cos(\theta)=\dfrac{4}{4\sqrt{2}}=\dfrac{1}{\sqrt{2}}=\dfrac{\sqrt{2}}{2}}\\\mathsf{sen(\theta)=\dfrac{4}{4\sqrt{2}}=\dfrac{1}{\sqrt{2}}=\dfrac{\sqrt{2}}{2}}\\\mathsf{\theta=\dfrac{\pi}{4}}\\\mathsf{\large~z_1=4\sqrt{2}\cdot\left[cos\left(\dfrac{\pi}{4}\right)+i\cdot sen\left(\dfrac{\pi}{4}\right)\right]}$

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