Complex conjugate of a complex function Does just replacing the $i$ ( $=\sqrt{-1}$ ) by $-i$ everywhere give the complex conjugate of any complex number of a function? Will that be the same as changing the sign of imaginary part of the finally computed complex value?

Let $f(z) = i z$. You're proposing writing
$$
g(z) = (-i) z
$$
and hoping that's the complex conjugate of $f$. Let's see it in parts. We have
$$
f(a + bi) = i(a + bi) = ai -b = -b + ai\\
g(a + bi) = -ai + b = b - ai
$$
But $\overline{-b + ai}$ is not $b - ai$, but is actually $-b - ai$.
So no, your proposed approach does not work, even for this very simple function.
