Algebra: Complex Numbers

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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. This is the Main Theorem of algebra.  In the Figure on the
right  the complex numbers plane  is shown with major players highlighted:  real 1  (red) and  imaginary i  (blue).
Lessons under this topic introduce you to the world of complex numbers.  Welcome!



Complex numbers plane


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