As students applied their learning of rational exponents, they discovered the problem of trying to take the square root of a negative number. As this solution does not exist in the real number system, students developed an understanding of imaginary numbers, specifically the number i (which is defined as the solution to the square root of -1).

Imaginary numbers have expanded the students ability to provide answers to previously unsolvable equations. With this understanding, students are now able to solve quadratics by providing a complex number solution, rather than the solution of “does not exist.”

Students are now using rational exponents in exponential equations and will soon be using logarithms to solve them.