## Complex Basics

This section introduces various notation and terms associated with complex numbers. As discussed above, complex numbers arise by introducing the square-root of as a primitive new algebraic object among real numbers and manipulating it symbolically as if it were a real number itself:*complex number*can be written as

*real part*and the

*imaginary part*. We may also use the notation

*complex multiplication*follows directly from the definition of the imaginary unit :

*e.g.*, . However, such formality tends to obscure the underlying simplicity of complex numbers as a straightforward extension of real numbers to include . It is important to realize that complex numbers can be treated algebraically just like real numbers. That is, they can be added, subtracted, multiplied, divided, etc., using exactly the same rules of algebra (since both real and complex numbers are mathematical

*fields*). It is often preferable to think of complex numbers as being the true and proper setting for algebraic operations, with real numbers being the limited subset for which .

**Next Section:**

The Complex Plane

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Fundamental Theorem of Algebra