# Use of Complex numbers in Engineering

1. Jun 4, 2014

### Ritvinder

Dear All,

Hi! I am about to begin a Diploma in Aeronautical Engineering and would like to know if anyone could help me understand if in my future career of being an Aeronautical Engineer I would at any time be required to use Complex numbers to solve problems. If yes can you suggest examples please.

Thankyou...

2. Jun 4, 2014

### donpacino

One example can be seen in aircraft control.

Look up what a phasor is. phasors are used extensively in engineering, and involve complex numbers.

Lets say you want to see how moving a spoiler on each wing will effect the dynamics of the aircraft. You can look at the system in the time domain, but that could result in a 3rd order differential equation (really complicated calculus). Instead you can look at the frequency response of the system. This frequency response will end up containing complex numbers, but it can tell you a lot about the system response AND you only need to use algebra to solve the problem.

3. Jun 4, 2014

### TheAustrian

This seems to be a common issue. I always advocate that complex numbers should be taught early in schools to make them more natural to people.

4. Jun 4, 2014

Complex numbers are quite important in the study of a number of topics in aerospace/aeronautical engineering. Wave-like phenomena are often represented by complex numbers and they are frequently used in the solution of certain differential equations. One of the most powerful mathematical concepts for engineers, the Fourier transform, relies in some sense on complex numbers.

Trust me, though, once you sit down and use them some more, they really aren't very tough.

There's a math joke in here somewhere...

5. Jun 4, 2014

### SteamKing

Staff Emeritus
I can't say if you'll use complex numbers on a daily basis as a practicing engineer, but your undergraduate curriculum is going to be chock full of courses containing complex algebra and the calculus of complex variables. In addition, your fluids dynamics courses are going to use complex analysis to solve various potential flow problems.

6. Jun 4, 2014

### analogdesign

Also, while you're not going to be manipulating complex numbers on a piece of paper much, you are going to be implicitly using them constantly because frequency and phase domain approaches are ALL OVER control and aerospace applications.

7. Jun 5, 2014

### homeomorphic

You can hit people over the head 1000 times with complex numbers the way they are usually taught in high schools and it's not going to help much. But teach them a couple times the way they are explained in chapter 1 of Visual Complex Analysis and poof. Problem solved. Assuming you can get them to understand it. No more silliness about arbitrary demanding that x^2+1 has to have a root for some odd reason.

8. Aug 18, 2014

### FactChecker

1) The theory of incompressible, irrotational flows is the starting point of understanding ideal aerodynamics. It requires complex analysis and conformal mappings.
2) determining stability of feedback systems requires understanding zeros and poles in locations in the complex plane.
3) (closely related to 2) Understanding the differential equations of flight dynamics requires solving differential equations using Laplace transforms. The frequencies are represented in the complex plane.