Final answer:
The correct set of fundamental functions, based on the rules of quantum mechanics and the given choices, is option 2) 1, 1, -1, i. This set aligns with the possible quantum number values and may include a phase factor represented by 'i'. Quantum numbers dictate the properties of electron orbitals in atoms.
Step-by-step explanation:
The question asks about the correct set of the fundamental functions for a given set of numbers, which appears to be related to quantum mechanics, specifically to the solutions of Schrödinger's equation for an electron in an atom. The given options are sets of numbers which likely represent the quantum numbers for the electron states. Quantum numbers are used to describe the properties of electron orbitals. In this case, the student is likely asked to find the fundamental set that can exist according to the quantum mechanical rules.
The options given are:
1) 1 i, 1 i, 1-i, i
2) 1, 1, -1, i
3) 1, 1, -1, -i
4) 1, 1, 1, i
Analyzing the options and knowing that quantum numbers must take certain forms, the correct answer would be option 2) 1, 1, -1, i. This set contains values that correspond to acceptable quantum numbers, with 1 and -1 representing possible values for orbital angular momentum quantum numbers (1) and their magnetic quantum numbers (m), and i representing the imaginary unit which might signify a phase factor in the wave function, not a quantum number.