Solving a Binomial Equation with the Mean and Difference of the Roots
The mean and difference of the roots of a binomial equation allow us to solve the equation.
So the radical part gives us the difference between a root and the mean. When m2<c, δ2<0 which means δ is not a real number since its square is negative. It is still useful to maintain that δ us a number of sorts and express it as a multiple of the solution of i2=-1. Setting i2=-1 makes i a magic number and mathematicians magicians.
Supplemental (Jan 5): What is so curious about the imaginary numbers is their surreal character.