Question

calcule
$\frac{1-i}{1+i}+ \frac{i}{i-2}$

Answer 1

$\frac{(1-i)((i-2)+i(1+i)}{(1+i)(i-2)}$ =$\frac{i-2+1+2i+i-1}{i-2-1-2i}$ =  $\frac{2+4i}{1-i}$ = $\frac{2+4i}{1-i}$ = $\frac{1+i}{1+i}$= $\frac{2+2i +4i-4}{1-i^{2}}$

simplificando tudo, fica:
$1+3i$