Maybe you've heard of an imaginary number, but what is it really? And how can it make any sense? In this course, we will explore the theory, intuition and applications that come from the famous $$\sqrt{-1}$$. The course starts off with the history and construction of numbers. We then learn how to work with complex numbers leading up to some surprising results. At the end of the course, we look at advanced concepts like holomorphic functions and Riemann surfaces. So come join! Along the way, we will also touch upon other important topics in mathematics including group theory and algebra and look at cool, useful real-life engineering applications.