The nomenclature of the complex $[CuCl_2(CH_3NH_2)_2]$ is

Dicholrobis(methylamine)copper(II)

The correct answer is Option (4) → Dicholrobis(methylamine)copper(II)

Let's determine the correct IUPAC name step by step for the complex:

Complex: $[CuCl_2(CH_3NH_2)_2]$

1. Identify the ligands:
• CH3NH2 → methylamine (neutral ligand)
• Cl⁻ → chloro (anionic ligand)
2. Count and use prefixes:
• 2 methylamine → bis(methylamine)
• 2 chloro → dichloro
3. Order of naming ligands:
• Anionic ligands first, then neutral ligands → chloro before methylamine.
4. Oxidation state of central metal (Cu):
• Chloride is -1 each, methylamine is neutral. Let oxidation state = x:

$x+2(−1)+2(0)=0  ⟹  x=+2$

• So, Copper(II)

5. Combine everything in proper IUPAC format:

• Ligands in alphabetical order (ignoring prefixes): chloro, methylamine
• Number of ligands indicated by di, bis
• Central metal + oxidation state → copper(II)