Fundamental Theorem of Algebra

An degree Polynomial has exactly complex roots (including multiplicity).

• Complex roots come in Complex Conjugate pairs
  • If is a root of a polynomial, then so is
  • For , , hence Real Numbers do not come in pairs because the “complex conjugate” of a real number is itself.

Complex Eigenstuff

Complex roots coming in complex conjugate pairs implies that complex Eigenvalues and their Eigenvectors come in complex conjugate pairs. This is because eigenvalues are the solutions to the Characteristic Equation, which is a Polynomial equation.