structural:summarization
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 numbers, imaginary numbers, 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

has solutions

Since − 3 {\displaystyle {\sqrt {-3}}} is not any real number, both of these solutions for x are complex numbers.