Use of Complex numbers in Engineering

In summary: The study of acoustics and sonochemistry is based on the understanding of complex waves and their behavior.
  • #1
Ritvinder
2
0
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...
 
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  • #2
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
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
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.

TheAustrian said:
I always advocate that complex numbers should be taught early in schools to make them more natural to people.

There's a math joke in here somewhere...
 
  • #5
Ritvinder said:
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...

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
SteamKing said:
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.

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
I always advocate that complex numbers should be taught early in schools to make them more natural to people.

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
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.
 

What are complex numbers?

Complex numbers are numbers that consist of a real part and an imaginary part. The imaginary part is represented by the letter "i" and is equal to the square root of -1.

How are complex numbers used in engineering?

Complex numbers are used in engineering to represent and solve problems involving alternating current (AC) circuits, signal processing, and control systems. They are also used in electromagnetic field analysis and fluid dynamics.

Why are complex numbers important in engineering?

Complex numbers allow engineers to efficiently model and analyze systems that involve oscillations, such as AC circuits and mechanical vibrations. They also provide a way to represent and manipulate quantities that have both magnitude and direction, such as electrical impedance and phasors.

What is the difference between a real and complex number in engineering?

In engineering, real numbers represent physical quantities, such as voltage and current, that are measurable in the real world. Complex numbers, on the other hand, are used to represent and analyze quantities that involve oscillations or have both magnitude and direction.

How are complex numbers represented and manipulated in engineering?

In engineering, complex numbers are typically represented using the rectangular form or the polar form. They can be manipulated using algebraic operations and specific rules for working with imaginary numbers, such as the concept of conjugates.

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