But why do these complex values describe?
To understand this, you need to study calculus. This is not just limited to cos(), all trigonometric functions exhibit this behaviour. In short, the domain of trigonometric functions can be extended to the complex plane, in which case the range of those functions will also span the complex plane (instead of usual [-1, 1]). The following are some links to show how trigonometric functions and complex numbers are interconnected
