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Imaginary Numbers Are Real [Part 1: Introduction] Lets say were given the function f(x) = x^2 + 1. We can graph our function and get a nice parabola. Now lets say we want to figure out where the equation equals zero we want to find the roots. On our plot this should be where the function crosses the x-axis. As we can see, our parabola actually never crosses the x-axis, so according to our plot, there are no solutions to the equation x^2+1=0. But theres a small problem. A little over 200 years ago a smart guy named Gauss proved that every polynomial equation of degree n has exactly n roots. Our polynomial has a highest power, or degree, of two, so we should have two roots. And Gauss discovery is not just some random rule, today we call it the FUNDAMENTAL THEOREM OF ALGEBRA. So our plot seems to disagree with something so important its called the FUNDAMENTAL THEOREM OF ALGEBRA, which might be a problem. What Guass is telling us here, is that there are two perfectly good values of
