Question

número complexos alguem????

Answer 1

$4 . (cos \frac{ \pi }{3} + i . sen \frac{ \pi }{3}) . 7. (cos \frac{ 5\pi }{3} + i . sen \frac{5 \pi }{3}) = \\ \\ 4 . (\frac{ 1}{2} + sen \frac{ \sqrt{3} }{2} . i) . 7. [- cos \frac{ \pi }{3} + i . (- sen \frac{\pi }{3})] = \\ \\ (4 . \frac{1}{2} + 4 . \frac{ \sqrt{3} }{2} . i) . 7. [- \frac{1}{2} + i . (- \frac{ \sqrt{3} }{2})] \\ \\ (2 + 2 \sqrt{3} i) . 7 . (- \frac{1}{2} - \frac{ \sqrt{3} }{2} i) = \\ \\ (2 + 2 \sqrt{3} i) . (- \frac{7}{2} - \frac{7 \sqrt{3} }{2} i) =$

Fazendo a multiplicação , temos:

$2 . (- \frac{7}{2} ) - 2 . \frac{7 \sqrt{3} }{2} i - 2 \sqrt{3} . \frac{7}{3} i - 2 \sqrt{3} . \frac{7 \sqrt{3} }{2} . i^{2} \\ \\ -7 - 7 \sqrt{3} i - \frac{- 14 \sqrt{3} }{3} i - 7 . ( \sqrt{3})^{2} . (- 1) = \\ \\ - 7 - \frac{21 \sqrt{3} - 14 \sqrt{3} }{3} i - 7 . 3 . (- 1) = \\ \\ - 7 - \frac{21 \sqrt{3} - 14 \sqrt{3} }{3} i + 21 =$


$- 7 + 21 - \frac{21 \sqrt{3} - 14 \sqrt{3} }{3} i + 21 = \\ \\ 14 - \frac{7 \sqrt{3} }{3} i$

Ou

$7 . ( 2 - \frac{ \sqrt{3} }{3} i )$


Espero ter ajudado