numeros complexos.

por fill2013 Qui 21 Nov 2013, 15:02

determine todos os numeros complexos w, tais que w^3= cos π + i sen π

por PedroCunha Qui 21 Nov 2013, 17:57

Da segunda Lei de Moivre, temos:

$\\ w^3 = \cos \pi + i \sin \pi \\\\\circ w = \cos \left(\frac{\pi + 2k\pi}{3} \right) + i\sin \left(\frac{\pi + 2k\pi}{3} \right )\\\\\text{Para k = 0:}\\\\w = \cos \frac{\pi}{3} + i\sin \frac{\pi}{3} \therefore w = \frac{1}{2} + \frac{\sqrt3}{2}i \\\\\text{Para k = 1:}\\\\w = \cos \pi + i\sin \pi \therefore w = -1 \\\\\text{Para k = 2:}\\\\w = \cos \frac{5\pi}{3} + i\sin \frac{5\pi}{3} \therefore w = \frac{1}{2} - \frac{\sqrt3}{2}i$

Att.,
Pedro

numeros complexos.

numeros complexos.

Re: numeros complexos.

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