Final answer:
The Fundamental Theorem of Algebra states that any polynomial function of degree n must have at least one zero in the complex number system.
Step-by-step explanation:
The statement you are referring to is known as the Fundamental Theorem of Algebra. It states that if f(x) is a polynomial function of degree n, then it has at least one zero in the complex number system. This means that every non-constant polynomial equation has at least one solution that is a complex number, which may be a real number if it falls on the real number axis within the complex plane.
Additionally, when referring to dimensional consistency in physics, every term in an equation must have the same dimensions which implies that the arguments of standard mathematical functions must be dimensionless. This concept is instrumental in ensuring that equations represent real, physically meaningful quantities, as seen in the context of potential energy functions where the zero can be conveniently placed.
The Fundamental Theorem of Algebra states that if f(x) is a polynomial function of degree n, then n has at least one zero in the complex number system. In other words, every polynomial of degree n has n complex roots, counted with multiplicity.
For example, the polynomial function f(x) = x^2 - 1 has degree 2 and has two complex roots: x = 1 and x = -1.
Therefore, the statement in the question is true for polynomial functions.