The IUPAC name of the complex [Ni(C₄H₇O₂N₂)₂] formed from the reaction of Ni²⁺ with dimethyl glyoxime is

bis (2,3-butanedione dioximato) nickel (II)

The IUPAC name of the complex [Ni(C4H7O2N2)2] formed from the reaction of Ni2+ with dimethyl glyoxime is: (4) bis(2,3-butanedione dioximato) nickel(II)

Now, let's describe the answer in more detail:

The answer (4) "bis(2,3-butanedione dioximato) nickel(II)" refers to the coordination complex formed between a nickel(II) ion (Ni2+) and two molecules of 2,3-butanedione dioxime ligand. In this complex, the nickel(II) ion acts as the central metal ion, while the 2,3-butanedione dioxime ligand is a bidentate ligand, meaning it can coordinate to the nickel ion through two of its donor atoms.

The IUPAC name is constructed as follows:

"bis" indicates there are two ligands of 2,3-butanedione dioxime coordinated to the nickel(II) ion.

"2,3-butanedione dioximato" describes the specific ligand that coordinates to the nickel(II) ion. This ligand is derived from 2,3-butanedione (also known as diacetyl), which has two oxime functional groups attached to it. The oxime functional groups (-C=N-OH) are the donor atoms that coordinate to the nickel(II) ion.

-"nickel(II)" indicates the oxidation state of the central metal ion, which is +2 in this complex.

Overall, the IUPAC name "bis(2,3-butanedione dioximato) nickel(II)" precisely identifies the composition of the coordination complex, helping chemists to understand its structure and properties in a standardized manner.