# The Complex Numbers

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## Abstract

The polynomial *x*^{2} + 1 does not have any roots within the set of real numbers. A new number, called *i*, is introduced as a root of that polynomial. The complex numbers are all the numbers of the form *a* + *bi* where *a* and *b* are real numbers. It is a remarkable fact that every polynomial with real coefficients (or even with complex coefficients) that is not a constant function has a root within the set of complex numbers. In this chapter, we develop the basic properties of the complex numbers.

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