Question

Números complexos:
Resolver
$[(1 + i)^2 + (1 - i)^2] ^{205}$

Answer 1

$i^2=-1\\ \\(1+i)^2=1+2i+i^2=1+2i-1=1-1+2i=2i\\ \\(1-i)^2=1+2i-i^2=1+2i-1=1-1-2i=-2i\\ \\ \\ \Big[(1+i)^2+(1-i)^2\Big]^{205}=\Big[2i+(-2i)\Big]^{205}=\Big[2i-2i\Big]^{205}=0^{205}=0$