Question

Forma trigonométrica z1 = 4 + 4i em radianos me ajudemmmm!!!!!!!!!!!!!!!

Answer 1

Explicação passo-a-passo:

$\sf z=4+4i$

$\sf |z|=\sqrt{4^2+4^2}$

$\sf |z|=\sqrt{16+16}$

$\sf |z|=\sqrt{32}$

$\sf |z|=4\sqrt{2}$

Temos que:

$\sf sen~\theta=\dfrac{4}{4\sqrt{2}}~\rightarrow~sen~\theta=\dfrac{\sqrt{2}}{2}$

$\sf cos~\theta=\dfrac{4}{4\sqrt{2}}~\rightarrow~cos~\theta=\dfrac{\sqrt{2}}{2}$

Desse modo, $\sf arg(z_1)=\dfrac{\pi}{4}~rad$

$\sf z=4\sqrt{2}\cdot\left[cos~\left(\dfrac{\pi}{4}\right)+i\cdot sen~\left(\dfrac{\pi}{4}\right)\right]$