For the majority of our math career we work solely with real numbers such as basic integers, decimals, fractions, and even pi. Real numbers can be represented on a numbers line. Then we looked at the use of imaginary units such i and Pi times i. Now we introduce the concept of complex numbers that basically crash both worlds together. For example, if we used the real numbers 8 and 1.5 and the imaginary unit 2i we could create a complex number in the form of x= 8(2i) + 1.5. Complex numbers make simplification nearly impossible in a lot of instances. One of the things students often overlook is that math is not an exact science and can, at times, be devised for expediency and theory. These types of representations are used in the fields of science and engineer all the time. Theoretical physics often uses all these forms of notation to represent physical phenomenon that they cannot see even with the strongest lens that technology could create. Electric current is often described in a similar way. One of the aspects that is often overlook is that imaginary numbers allow us to create weather forecast models. Those big moving patterns of weather we take for grant on the morning newscasts are all driven by this type of work. Trajectories of many different things, including weather, depend on abstract modelling that is made possible by you guessed it complex numbers. Another application that is currently being explored by many scientists is how to predict behaviors that follow some sort of pattern. Guess what form of math they use when modelling these behaviors?

Below you will find basic and advanced uses of complex numbers. We will show you how to perform basic mathematical operations with these values. You will also see how to convert these values back to a standard form that is much more recognizable for most students. We will explore how they are affected by absolute value symbols. You will also learn how to chart these in a graphically form that will lead you to developing full scale models.