In previous lectures we have seen that quadratic equations that have no solutions when only real values are considered, do have solutions when complex numbers are allowed as input and output values. In this lecture, we check the complex solutions to a quadratic equation using the complex arithmetic operations we have studied. We then show methods of creating graphs that allow us to visually represent the characteristics of this complex function. These include a novel animated graphing technique developed for this lecture that provides an intuitive understanding of a complex function's behavior.