Actually, I am facing a problem with a wrong implication/fallacy in complex number, which is
$\frac{1}{i}=\frac{1\times i}{i\times i}=\frac{i}{i^2}=\frac{i}{-1}=-i\implies i=-i$
I know I should not ask this kind of question here, but I want to learn the reason behind this type of unwanted fallacies.
Can anybody help me? Thanks for your assistance in advance.