A complex number is a number that contains a real part and an imaginary part. The imaginary part of a complex number contains the imaginary unit, ı . This number is called imaginary because it is equal to the square root of negative one. ı is not a real number. Although it is rarely, if ever, used in some fields of math, it comes in very handy when calculating the roots of polynomials, because the quadratics that were previously irreducible over the reals are reducible over the complex numbers. Before we get into that, though, we'll learn about the imaginary unit ı , the complex plane, and a few operations involving complex numbers. Then we'll be able to understand the true usefulness of complex numbers.