Complex numbers
Subject:
Algebra [1]
Complex numbers were invented to enhance the set of real numbers and make it possible that every quadratic equation has a root. Arithmetic operations of addition, subtraction, multiplication and division were introduced in the set of complex numbers such a way that they agree and extend those operations over real numbers. A wonderful geometric presentation of complex numbers does exist, as well as a nice geometric interpretation of arithmetic operations. Even raising the power and taking roots is possible over the complex domain. A remarkable fact is that every polynomial equation with complex coefficients has a complex root. Moreover, every polynomial equation has exactly n roots, where n is the equation degree, and all these roots are complex numbers.