Question

Considerando os Números Complexos r = 1 + i e s = 1 - i, pode-se afirmar que o produto r¹² . s¹¹ vale:
a) r
b) -r
c) 2r
d) 2s
e) s

Answer 1

Olá Keymin,
bom dia!

$\\r^{12}\cdot\,s^{11}=\\\\r^{11}\cdot\,r^1\cdot\,s^{11}=\\\\(r^{11}\cdot\,s^{11})\cdot\,r=\\\\(r\cdot\,s)^{11}\cdot\,r=\\\\((1+i)(1-i))^{11}\cdot\,r=\\\\(1-i^2)^{11}\cdot\,r=\\\\(1-(-1))^{11}\cdot\,r=\\\\\boxed{2^{11}r}$