complex roots of quadratic

Hi there,

I've been looking at complex numbers, really fascinating stuff!

While I understand the general idea behind complex numbers, I'm struggling to see how the complex roots of the quadratic work.

See image below of the plot of the quadratic, I've drawn a red point where the complex number lies, but what about the complex number ?

Am I looking at this the wrong way? What exactly do the complex roots mean in the solution of the above quadratic?

http://www.forumsigs.com/users/rgbag...plex_roots.jpg

Looking forward to a response!