Question

alguém me ajudaaaaa pelo amor de Deus, rápido​

Answer 1

Explicação passo-a-passo:

$\sf \dfrac{7\pi}{6}=\dfrac{7\cdot180^{\circ}}{6}=\dfrac{1260^{\circ}}{6}=210^{\circ}$

• $\sf sen~210^{\circ}=-sen~(210^{\circ}-180^{\circ})$

$\sf sen~210^{\circ}=-sen~30^{\circ}$

$\sf sen~210^{\circ}=-\dfrac{1}{2}$

• $\sf cos~210^{\circ}=-cos~(210^{\circ}-180^{\circ})$

$\sf cos~210^{\circ}=-cos~30^{\circ}$

$\sf cos~210^{\circ}=-\dfrac{\sqrt{3}}{2}$

Assim:

$\sf z=2\sqrt{2}\cdot\Big[cos~\Big(\dfrac{7\pi}{6}\Big)+i\cdot sen~\Big(\dfrac{7\pi}{6}\Big)\Big]$

$\sf z=2\sqrt{2}\cdot\Big[-\dfrac{\sqrt{3}}{2}+i\cdot \Big(-\dfrac{1}{2}\Big)\Big]$

$\sf z=-\dfrac{2\sqrt{6}}{2}-i\cdot\dfrac{2\sqrt{2}}{2}$

$\sf \red{z=-\sqrt{6}-i\cdot\sqrt{2}}$