Question

Obtenha a forma algébrica de Z= 4(cos 120° + i sen 120°)

Answer 1

Cos 120º = - Cos 60º = -1/2

Sen 120º = Sen 60º = (√3)/2

$Z = 4 ( \frac{1}{2} + \frac{ \sqrt{3} }{2} i) = 2 + 2 \sqrt{3} i$

Answer 2

É só substituir o valor do seno, cosseno, e aplicar a distributiva
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$cos~120\º=-cos~60\º=-1/2\\sen~120\º=sen~60\º=\sqrt{3}/2$
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$z=4(cos~120\º+i*sen~120\º)\\\\z=4(-\frac{1}{2}+i*\frac{\sqrt{3}}{2})\\\\z=4*(-\frac{1}{2})+4i*\frac{\sqrt{3}}{2}\\\\z=-2+2i*\sqrt{3}\\\\\boxed{\boxed{z=-2+(2\sqrt{3})i}}$