Step 1: Understand the effective atomic number (EAN).
The EAN is calculated as the sum of the number of electrons donated by the ligands and the number of valence electrons of the central metal. In this case, \( \text{NH}_3 \) donates 2 electrons per ligand.
Step 2: Calculation.
The EAN of cobalt in the complex is calculated as:
\[
\text{EAN} = 27 + (6 \times 2) = 33
\]
Final Answer:
\[
\boxed{33}
\]