This unit strives to answer a key question posed in Unit 3, “What is the square root of a negative number?” Imaginary numbers are introduced to help answer this question. Together real numbers and imaginary numbers make up the complex number system. It is now possible to find the square root of a negative number using the imaginary part I, knowing I = sqrt(-1). With the concept of the complex number systems comes the complex plane, on which the vertical axis is the imaginary axis and the horizontal axis the real axis. A connection to Unit 3 is made when deriving of the powers of i. Operations with complex numbers, such as multiplication, will rely on simplifying powers of I greater than one, i.e. i^2=-1. When dividing by a complex number, it will be necessary to multiply both the numerator and the denominator by the denominator’s complex conjugate to move the imaginary part from the denominator. Multiplying a complex number by its conjugate will result in a real number. Complex numbers will be important in future courses of algebra, geometry, mathematical analysis, science, and engineering.