The Fundamental Theorem of Algebra states that every non-constant polynomial equation with complex coefficients has at least one complex root. This means that if you have a polynomial of degree n , it will have exactly n roots when counted with their multiplicities. This theorem is significant because it guarantees that polynomial equations can be solved within the set of complex numbers, which includes all real numbers as well. It highlights the relationship between algebra and complex analysis, showing that the behavior of polynomials is deeply connected to the complex number system.