Imagining the roots of a quadratic
The real roots of a quadratic equation are symmetrically either side of the vertical line of symmetry through the vertex. In the case of a quadratic equation with complex roots these can be displayed by finding the intersection of the x-axis and an "imagined" negative quadratic with the same vertex (i.e. the reflection of the original quadratic in the horizontal line through the vertex). These horizontal distances either side of the line of symmetry can be interpreted as "imaginary" distances.
A dynamic demonstration of this:
Further information
This idea is taken from "Imagine the roots of a quadratic" from 'PIG' and other tales, The Mathematical Association, 1997.
