Step 1: Recall the meaning of conjugate base.
A conjugate base is formed when an acid loses one proton.
That is,
\[
\text{Acid} \rightarrow \text{Conjugate base}+H^+
\]
Step 2: Remove one proton from ammonia.
For ammonia,
\[
NH_3
\]
On losing one proton,
\[
NH_3 \rightarrow NH_2^- + H^+
\]
Thus, the conjugate base of \(NH_3\) is
\[
NH_2^-
\]
Step 3: Check the other options.
\[
NH_4^+
\]
is the conjugate acid of \(NH_3\), because it is formed by accepting one proton.
\[
NH_4OH
\]
is ammonium hydroxide, not the conjugate base of ammonia.
\[
NH_2
\]
does not represent the proper charged conjugate base.
Step 4: Final conclusion.
Therefore,
\[
\boxed{NH_2^-}
\]
Hence, the correct option is (3).