Editing Elementary algebra (section)

====Complex numbers====

All quadratic equations have exactly two solutions in [[complex numbers]] (but they may be equal to each other), a category that includes [[real number]]s, [[imaginary number]]s, and sums of real and imaginary numbers. Complex numbers first arise in the teaching of quadratic equations and the quadratic formula. For example, the quadratic equation

:<math>x^2+x+1=0</math>

has solutions

:<math>x=\frac{-1 + \sqrt{-3}}{2}  \quad \quad \text{and} \quad \quad x=\frac{-1-\sqrt{-3}}{2}.</math>

Since <math>\sqrt{-3}</math> is not any real number, both of these solutions for ''x'' are complex numbers.