So I'm taking my complex variables class and learning about these cool powerful theorems like the Cauchy Goursat theorem. I know this all has huge application in physics however I just don't know what they are. Currently I'm only taking freshmen E@M so I know I won't be using it there. But next semester I'm taking analytical mechanics and I want to start using the math I know for my physics. So what are some application of complex variables to physics?