Square roots of negative numbers gave us the spectacular Mandelbrot set*, so there is nothing to be laughed at. Negative numbers also find a lot of use around here, using Centigrade system in the near Arctic.
More and more mathematics is needed in the future, people who think otherwise are freeloaders depending on others doing the right and necessary things in engineering and research benefitting everybody. I am sure there is fairly high level math at work in the background of Google search algorithms, not to mention Lightroom clarity slider. Somebody has to optimize the algorithms in navigators we take for granted. The list is endless.
I was a national math contest finalist in my junior high days, as have been two of my sons out of three, who are now successfully studying engineering. It seems that the gap between the people who understand, at least in principle, how things work and how the modern society works as a result, and those who just could't care less is widening. That is not good.
*) I wrote a simple program in -85 or so which drew a B&W picture of the set on a high resolution Hercules graphics screen, a whooping 720×348 pixels. With 100 iterations per point it took about 8 hours of 8086 processor time.