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.
Complex numbers
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.
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