Question

(UFV-MG) Calculando a expressão ($\frac{(i+1)^{2} (2i-1)i^{3}}{(i+1)(i-1)} + 2i$
Obtém-se:
a) 1
b) zero
c) 4i+1
d) -1
e) 4i-1

Answer 1

Primeiramente, devemos lembrar que:

$\boxed{i^2=-1}$

$\frac{(i+1)^2(2i-1)i^3}{(i+1)(i-1)}+2i\\\\ \frac{(i^2+2i+1)(2i-1)i^2*i}{i^2-1}+2i\\\\ \frac{(-1+2i+1)(2i-1)-i}{-1-1}+2i\\\\ \frac{2i(2i-1)-i}{-2}+2i\\\\ \frac{-2i^2(2i-1)}{-2}+2i\\\\ \frac{2(2i-1)}{-2}+2i\\\\\ -(2i-1)+2i\\\\ -2i+1+2i\\\\ \boxed{1}$