Normalization constants in physics are typically real-valued because they normalize measurable quantities, which are inherently real. However, it is possible to express equations using complex numbers, particularly in fields like electrical engineering and vibration engineering, where complex normalization can simplify calculations and improve computational efficiency. While real numbers and vectors are standard due to their simplicity and familiarity, complex numbers are increasingly recognized for their utility in various applications. The discussion highlights that complex numbers can be essential in certain contexts, even if they are not always the preferred representation. Ultimately, both complex numbers and vectors have their place in mathematical formulations, depending on the specific requirements of the problem at hand.