Conclusion
Complex analysis specifically Geometry in the Complex Plane, is important because it displays predictions that can help us predict the world around us. We can apply certain different inputs and predict the outputs. In real life this applies because we are given certain inputs and we solve for the possible outputs and use the ones that are the most viable to the situation. If we were to continue this research we would have learned more about the hyperbolic plane and how that relates to Mobius functions.