Complex Numbers An introduction to complex numbers is the content of the video Complex numbers 1. When one works with real numbers long enough, one starts to realize that the real number system has limitations. In particular, there are polynomials with coefficients in R that have no roots in R . For example, the polynomial p(x)=x2 1 has Answer 1 Question 1 real roots. Indeed, by definition, any root of p(x) would be a solution to the equation x2 1=0 or equivalently x2=1, but this has Answer 2 Question 1 real solutions, since in the real numbers we Answer 3 Question 1 take square roots of negative numbers. So if we want to be able to solve the equation x2=1 , then we would need a new number system in which we can take square roots of 1