One of the most important properties of complex numbers is algebraic closure, which is the achievement of Dr. Gauss's thesis-the basic theorem of algebra. Other numbers, such as real numbers, do not have this property. Numbers wider than complex numbers, such as quaternions, do not satisfy the multiplicative commutative law. More importantly, the analysis based on complex numbers is particularly good and related to potential theory. If the relationship between quantum mechanics and complex Hilbert space is a suitable tool of quantum mechanics.