When we try to think of an inverse of the squaring function, we encounter two difficulties. One problem is that the reflection of the parabola y = x^2 is, in many places, double-valued, and, thus, not a function. Second, this plot does not explore negative input values. When we attempt to address this second difficulty, we develop the idea of the imaginary root i, which, when squared, gives -1. Knowledge of the imaginary root because will help us to study oscillatory dynamics in a later slide deck.