This is a community where INTJs can meet others with similar personalities and discuss a wide variety of both serious and casual topics. If you aren't an INTJ, you're welcome to join anyway if you would like to learn more about this personality type or participate in our discussions. Registration is free and will allow you to post messages, customize your account and use other features only available to our members.
Complex analysis is REALLY interesting imo. Real analysis can get kinda clunky in that differentiability, integrability, and analyticity, etc. are all separate things, but when you extend functions to the complex plane they all become synonymous. There are a lot of cool things like that. I don't know what parts of it would be useful for ChemE (besides the process control aspect), but it's been pretty invaluable for me in understanding Laplace and Fourier transforms and linear systems theory.
Real analysis is also good, but you don't get to the good stuff until much later, like with measure theory, Lp spaces, etc. (even then, only useful if you're into theory, like me!) Complex analysis will probably seem more useful right off the bat.