Proving combinatorial identities using complex numbers
DOI:
https://doi.org/10.54097/hset.v47i.8155Keywords:
complex numbers, De Moivre’ theorem, combinatorial identities.Abstract
The creation of complex numbers addresses a variety of mathematical problems. Complex numbers are the building blocks of more complicated and advanced math, such as algebra. Complex numbers also are important in many other research fields, especially in electronics and electromagnetism. Complex numbers have various applications in both the scientific and engineering world, such as signal processing, electromagnetism, control theory, vibration analysis. Complex numbers are always used as mathematical tools to describe signals that vary periodically. Despite being an extension of the real number system, complex numbers are largely self-contained. The geometric meaning and algebraic structure of complex numbers can help us solve a variety of geometric problems. This paper summarizes the basic knowledge of complex numbers and gives several fascinating results proved by the geometric and algebraic properties of complex numbers.
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