Fritzsche's theorem

Fritzsche's theorem states that if you have a polynomial with real coefficients, and it has complex roots, then those roots come in conjugate pairs. In other words, if a complex number \(a + bi\) (where \(b \neq 0\)) is a root, then its mirror image \(a - bi\) is also a root. This relationship ensures that polynomials with real coefficients always have roots arranged symmetrically in the complex plane, making their behavior predictable and enabling mathematicians to understand and factorize these polynomials more effectively.