# What is Complex Analysis? Why is it accompanied by Linear Algebra?

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.

Thanks

• I think it's quite rare to combine complex analysis with linear algebra, at least in the States, and not particularly natural. – Kevin Carlson Mar 23 '16 at 2:03
• I would say it would be good to take a standard linear algebra course in order to prepare for a course like complex analysis. How does complex analysis fulfill the linear algebra requirement? I wouldn't know, other than if someone if very fluent in complex analysis, this person should have zero issues in a standard lin algebra course. As far as your last sentence is concerned: It is worth pursuing complex analysis if you can because it is a magnificent field of math in my opinion. – imranfat Mar 23 '16 at 2:10

## 1 Answer

Back when I studied Complex Analysis, I was always intently searching for real-world applications, as I relied on them to help me grasp many of the key concepts and theories. Perhaps more than my peers, I had difficulty understanding theories presented in a purely abstract manner, and I'm afraid that I annoyed the daylights out of my professor with my frequent request for illustrative examples/applications. Having said all that, I later found that complex analysis very nicely applied to the field of electrical engineering, particularly in the study of Alternating Current (AC) systems, such as motor and generator operating principles.

• It is also incredibly useful in evaluating some of the integrals within the (perhaps too abstract for some) field of Quantum Field Theory. – Thomas Russell Mar 3 '17 at 17:22