ABSTRACT
Having no solutions to a simple equation in real numbers was long since a signal to mathematicians that we needed to move beyond real numbers and widen the domain in which possible solutions to real number equations can exist. This is accomplished by simply allowing the number -1 to be defined as an “imaginary” number and then building a wider domain using that single number. Complex numbers have a real part and an imaginary part. This chapter addresses the question: Does the expansion of the real numbers using the square root of -1 help us find solutions of polynomial equations beyond quadratic (i.e., degree 2) equations? The answer is yes. The complex numbers play a central role in all of mathematics, not least of all because they contain all the possible solutions to every polynomial equation over complex numbers, and hence over real numbers.
