For my Complex Analysis course, we are to look up applications of Complex Numbers in the real world. The semester has just started and I am still new to the complex field. I want to get a head start on my research for the course. Anything I have seen on the complex field has only been in passing from my other course like ODE, Linear Algebra, and Abstract Algebra. I was wondering if someone can lead me into the right direction about what applications of complex numbers I can look into for my research topic. Recommended books I can refer to would also help.
Thank you for your time and thanks in advanced for your feedback.
Best Answer
The Schrodinger Equation from quantum physics is most neatly written using complex numbers and the (complex-valued) field $\psi$
$$i \hbar \frac{\partial}{\partial t} \psi = \hat{H} \psi$$
It is possible to split this equation up into a few real-valued equations, but you lose some elegance in the process.