Imaginary Roots and Graphs

[DJBruce]

So today I was bored in class so I started to think about polynomials, specifically parabolas. I know that it is possible to find imaginary roots of a parabola. My question is when you graph this parabola that has two imaginary roots the curve never hits the x-axis then were are the imaginary roots at? When I asked my instructor he said he had no idea. My only guess was that there was a z-axis there the appeared somewhere but I really have no ideas. So where are the imaginary roots on the graph?

[ydoaPs]

You can't find them graphically as the axes are real.

[DJBruce]

So if the axes where complex numbers then they would be there correct.

[AlphaNumeric]

Except that axes are 1 dimensional entities and if you made them complex numbers then they would have to be 2 dimensional!

 

So you would have to plot a 4 dimensional graph, because your axes would become 2 dimensional planes. This is why it's often so much more difficult to do complex analysis, it's hard to conceptualise the extra degrees of freedom.

[the tree]

Since you're only interested in what values x must take for f(x) to be zero: you could do it with three axis, Re(x) Im(x) and |f(x)|.

 

edit see attachment of a plot of |f(x+iy)|, where f(x):=x²+2x+5 and has complex roots.

Edited November 9, 2008 by the tree
i dun a pichur