I am not sure where to begin on this: Determine the images of all conic sections with a focus at the origin under the principal branch of the complex square root. I probably have to use the formula u(x, y) + i v(x, y) = sqrt((x, y)) and view square roots via the polar form. Any and every suggestion is appreciated. Thanks!
Polar form sounds like a good idea. Then you need to know what the conic sections look like in polar coordinates: http://en.wikipedia.org/wiki/Conic_section#Polar_coordinates.