:) Personally I've never used any serious complex analysis in my job (I'm very grateful too, because I always struggled a bit with it). The closest thing I've seen, which I did run into recently, is the use of complex numbers to compute very accurate finite differences. It's one of those delightful tricks that is both elegant and useful: https://blogs.mathworks.com/cleve/2013/10/14/complex-step-di...

I've been working in golang, which fortunately has built-in complex128 types, so it's proved very helpful in a project!