O número complexo( valendo 50 pontos, com resolução explicativa)
é igual a:
a) - i.
b) 1.
c) - 1.
d) i.
Soluções para a tarefa
Respondido por
1
Boa noite!
Solução!
![\left ( \dfrac{1+i}{1-i} \right )^{33}\\\\\\\
\left ( \dfrac{(1+i)\time(1+i)}{(1-i)\times(1+i)} \right )^{33}\\\\\\\
\left ( \dfrac{(1+i+i+i^{2} )}{(1+i-i-i^{2} )} \right )^{33}\\\\\\\
\left ( \dfrac{(1+2i+i^{2} )}{(1-i^{2} )} \right )^{33}\\\\\\\
Lembrando~~que~~i^{2}=-1\\\\\\\
\left ( \dfrac{(1+2i-1 )}{(1-(-1)} )} \right )^{33}\\\\\\\
\left ( \dfrac{(2i )}{(1+1)} )} \right )^{33}\\\\\\\
\left ( \dfrac{(2i )}{(2 )} \right )^{33}\\\\\\\
(i)^{33}=i \\\\\\\\\\
Resposta:Alternativa~~D](https://tex.z-dn.net/?f=%5Cleft+%28+%5Cdfrac%7B1%2Bi%7D%7B1-i%7D+%5Cright+%29%5E%7B33%7D%5C%5C%5C%5C%5C%5C%5C%0A+%5Cleft+%28+%5Cdfrac%7B%281%2Bi%29%5Ctime%281%2Bi%29%7D%7B%281-i%29%5Ctimes%281%2Bi%29%7D+%5Cright+%29%5E%7B33%7D%5C%5C%5C%5C%5C%5C%5C%0A+%5Cleft+%28+%5Cdfrac%7B%281%2Bi%2Bi%2Bi%5E%7B2%7D+%29%7D%7B%281%2Bi-i-i%5E%7B2%7D+%29%7D+%5Cright+%29%5E%7B33%7D%5C%5C%5C%5C%5C%5C%5C%0A+%5Cleft+%28+%5Cdfrac%7B%281%2B2i%2Bi%5E%7B2%7D+%29%7D%7B%281-i%5E%7B2%7D+%29%7D+%5Cright+%29%5E%7B33%7D%5C%5C%5C%5C%5C%5C%5C%0ALembrando%7E%7Eque%7E%7Ei%5E%7B2%7D%3D-1%5C%5C%5C%5C%5C%5C%5C%0A%5Cleft+%28+%5Cdfrac%7B%281%2B2i-1+%29%7D%7B%281-%28-1%29%7D+%29%7D+%5Cright+%29%5E%7B33%7D%5C%5C%5C%5C%5C%5C%5C%0A%5Cleft+%28+%5Cdfrac%7B%282i+%29%7D%7B%281%2B1%29%7D+%29%7D+%5Cright+%29%5E%7B33%7D%5C%5C%5C%5C%5C%5C%5C%0A%0A%0A+%5Cleft+%28+%5Cdfrac%7B%282i+%29%7D%7B%282+%29%7D+%5Cright+%29%5E%7B33%7D%5C%5C%5C%5C%5C%5C%5C%0A%28i%29%5E%7B33%7D%3Di+%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%0AResposta%3AAlternativa%7E%7ED+ "\left ( \dfrac{1+i}{1-i} \right )^{33}\\\\\\\
\left ( \dfrac{(1+i)\time(1+i)}{(1-i)\times(1+i)} \right )^{33}\\\\\\\
\left ( \dfrac{(1+i+i+i^{2} )}{(1+i-i-i^{2} )} \right )^{33}\\\\\\\
\left ( \dfrac{(1+2i+i^{2} )}{(1-i^{2} )} \right )^{33}\\\\\\\
Lembrando~~que~~i^{2}=-1\\\\\\\
\left ( \dfrac{(1+2i-1 )}{(1-(-1)} )} \right )^{33}\\\\\\\
\left ( \dfrac{(2i )}{(1+1)} )} \right )^{33}\\\\\\\
\left ( \dfrac{(2i )}{(2 )} \right )^{33}\\\\\\\
(i)^{33}=i \\\\\\\\\\
Resposta:Alternativa~~D")
Boa noite!
Bons estudos!
Solução!
Boa noite!
Bons estudos!
thaispissolato:
viu no gabarito a resposta certa é a D, i
Vou dar uma olhada!
Desculpe! Falta de atenção.
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