Question

Números Complexos?
Desenvolva:

Answer 1

$(\dfrac{-1+ \sqrt{2} i}{2} )^{3} = \dfrac{ (-1+ \sqrt{2} i)^{2} .(-1+ \sqrt{2} i)}{8}$$= \dfrac{ (1-2\sqrt{2} i+2 i^{2} ).(-1+ \sqrt{2} i)}{8} = \dfrac{ (1-2\sqrt{2} i-2 ).(-1+ \sqrt{2} i)}{8}$$= \dfrac{ (-1-2\sqrt{2} i ).(-1+ \sqrt{2} i)}{8} = \dfrac{1- \sqrt{2} i +2 \sqrt{2} i-4 i^{2} }{8}$$= \dfrac{1+\sqrt{2} i+4 }{8} = \dfrac{5+\sqrt{2} i}{8}$