The hybridization of nickel in [Ni(CO)4] and [Ni(CN)4]2- complexes is sp3 and dsp2, respectively.

Explanation:
The hybridization of an atom is determined by the number of electron pairs surrounding it. In both [Ni(CO)4] and [Ni(CN)4]2- complexes, the nickel atom is in the center surrounded by ligands.

1. [Ni(CO)4]:
In the [Ni(CO)4] complex, there are four carbon monoxide (CO) ligands attached to the central nickel atom. Each CO ligand donates a lone pair of electrons to the nickel atom, resulting in four electron pairs surrounding the nickel.

To determine the hybridization, we count the number of electron pairs and determine the hybrid orbitals needed to accommodate them. In this case, the nickel atom has four electron pairs, which can be accommodated in four hybrid orbitals. Therefore, the hybridization of nickel in [Ni(CO)4] is sp3.

2. [Ni(CN)4]2-:
In the [Ni(CN)4]2- complex, there are four cyanide (CN-) ligands attached to the central nickel atom. Each CN- ligand donates a lone pair of electrons to the nickel atom, resulting in four electron pairs surrounding the nickel.

Again, we count the number of electron pairs and determine the hybrid orbitals needed. In this case, the nickel atom has four electron pairs, which can be accommodated in four hybrid orbitals. However, the presence of the negative charge on the complex suggests that one of the hybrid orbitals must be unhybridized and contain a lone pair of electrons. This unhybridized orbital is a d orbital.

Therefore, the hybridization of nickel in [Ni(CN)4]2- is dsp2, where d represents the unhybridized d orbital and sp2 represents the hybrid orbitals.

In summary:
[Ni(CO)4] has sp3 hybridization, where the nickel atom forms four sigma bonds with the CO ligands.
[Ni(CN)4]2- has dsp2 hybridization, where the nickel atom forms four sigma bonds with the CN- ligands and has one unhybridized d orbital containing a lone pair.

Note: The presence of a negative charge in [Ni(CN)4]2- indicates the addition of an extra electron, which fills the unhybridized d orbital. This results in a diamagnetic complex.