I hope this doesn't extend to a lengthy question. I studied Linear Algebra recently in my first term at university. I came to the realization however that some institutions would teach that course during the second year while including what's known as "Complex Analysis".
I've tried looking it up and even ask about it -- and I am yet to understand how useful is that, specifically for Engineers. Why would someone teach complex analysis alongside linear algebra, and how does it "fulfill" the Linear Algebra course.
While I did take a brief introduction to complex numbers and whatnot, I can't seem to understand how crucial complex analysis would have been -- in fact, the only thing that stood out to me is the Cauchy-Integrals and some Methods of Contour Integrals. Keep in mind that I do expect I will encounter some applications of complex analysis further down the road, but all I need to know is whether it's worth dedicating portion of the course to.