TITLE: Graphically solving for complex roots -- how to visualize?
QUESTION [9 upvotes]: So recently we've been doing the complex roots of quadratics, cubics and polynomials in general in school. But my question is, is there a way to see where these roots are, just like you can see where the real roots are by seeing where they intercept with the X-axis?

For example, in this cubic here, it is evident that there is a real root just under -1, but is there a way to visualise the complex roots? Is there another line (similar to the x-axis) which intercepts the equation in another dimension?

REPLY [4 votes]: I have developed a very clear method of visualizing where the complex roots of an equation are. The method involves drawing a graph of y = f(x) in the usual way on x, y plane but adding a 3rd axis to allow those special complex x values which also produce real y values. This means we have a normal y AXIS but a complex x PLANE.
This is my first time on stackexchange so I cannot yet provide you with some excellent diagrams showing this method. I have however, just made a short video showing how the method works. I encouraging you to view it.
Solutions of Cubics using Phantom Graphs
http://screencast.com/t/dkAYxFDwH
Also, I have written a special section on this exact topic in my website:         http://www.phantomgraphs.weebly.com
just scroll right down to the last entry I have made especially for this question.