Question

Calcule os valores das potências z², z³ e z^9, sabendo que z = 2(cosπ/3 + i sen π/3).​

Answer 1

 Propriedade utilizada:

• $z^n=p^n\cdot(\cos (n\cdot\theta)+i\cdot\sin(n.\theta))$

                -x-

a -

$z^2=2^2\cdot(\cos(\dfrac{2\cdot\pi}{3})+i\cdot\sin(\dfrac{2\cdot\pi}{3}))\\z^2=4\cdot(\cos(\dfrac{2\cdot\pi}{3})+i\cdot\sin(\dfrac{2\cdot\pi}{3}))$

b -

$z^3=2^3\cdot(\cos(\dfrac{3\cdot\pi}{3})+i\cdot\sin(\dfrac{3\cdot\pi}{3}))\\z^3=8\cdot(\cos(\pi)+i\cdot\sin(\pi))$

c -

$z^9=2^9\cdot(\cos(\dfrac{9\cdot\pi}{3})+i\cdot\sin(\dfrac{9\cdot\pi}{3}))\\z^9=512\cdot(\cos(3\cdot\pi)+i\cdot\sin(3\cdot\pi))$

Dúvidas só perguntar!