Question

Escreva os seguintes números complexos na forma algébrica: a)z=8 (cos π/2 + π/2) b)z=2√3 (cos 4π/3 + sen 4π/3) ajudaaaaaaaaaaaaaaaaaaaaa

Answer 1

Explicação passo-a-passo:

a)

$\sf z=8\cdot\left[cos\left(\dfrac{\pi}{2}\right)+i\cdot sen~\left(\dfrac{\pi}{2}\right)\right]$

$\sf z=8\cdot(0+i\cdot1)$

$\sf z=8i$

b)

$\sf z=2\sqrt{3}\cdot\left[cos\left(\dfrac{4\pi}{3}\right)+i\cdot sen\left(\dfrac{4\pi}{3}\right)\right]$

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

$\sf z=-\dfrac{2\sqrt{3}}{2}-i\cdot\dfrac{2\cdot3}{2}$

$\sf z=-\sqrt{3}-3i$