How are imaginary numbers used in aerospace engineering?

Complex numbers are widely used in electrical engineering and control engineering (a subset of EE). These are both applicable to aerospace.

Imaginary Engineering

some comments.

"..I tend to call imaginary numbers, complex numbers, but they're the same thing."

.. NO.

"real" numbers have imaginary part = 0.

"imaginary" numbers have real part = 0.

complex numbers have both real and imaginary parts.

and dont be confused by the wording, imaginary numbers are just as real.

resistance (no, "impedance") is specified using a number in the form a+bj ("j" used instead of "i"), and that the imaginary part increases as the Hertz of the current flow increases.

J is used in electronics, where i means current.

I tend to call imaginary numbers, complex numbers, but they're the same thing.

Complex numbers can be thought of as vectors as well as "numbers". Basically a way of grouping two things together and treating them as a single object. Turns out much of the maths of complex numbers is the same as for 2D vectors, and vector maths gets used *a lot* in engineering. all you need to do to convert is see "i" as a unit vector (has length 1) that's perpendicular to a unit vector along the real part.

http://en.wikipedia.org/wiki/Unit_vector

You're right that complex numbers get used in investigating vorticies.They can be used subsonic and supersonic, if the behaviour of the flow in those different regimes is modeled (and some of the models aren't entirely worked out yet- lookup Navier–Stokes equations http://en.wikipedia.org/wiki/Navier%E2%80%93Stokes... . They work well in many situations, but there's times, when it's not clear at all what's going on, and as yet it's beyond top mathematicians to understand how to fix it, let alone engineers!)

A vortex is a description of a type of flow, so you need a way of mathematically representing flow,so it can be looked at. a flow can be represented as something called a vector field. A vector field takes a bit of thinking to understand, but it's like a formulae which if provided with the location of a point returns a vector showing which direction the flow is moving at a particular point.

2D problems are usually mathematically easiest to work with/solve, but it's easiest to visualise a vector field in 3D. Consider how you might like to describe the *flow* of air around a room. Due to how warm air rising in some places it's like to flowing up, other places it's likely to falling. Other places it's likely to going left, other places right. If you take the vector field that describes the flow of air around the room, and feed it a position, you'll get a vector that represents the position the air is moving at that point.

Back to complex numbers. the flow over a wing can (often) be assumed to be a 2D problem of flow around the wing's cross section.(ie assume air doesn't flow in/out of the page) The flow is then a 2D vector field. Turns out there's a lot of mathematical techniques that are easy to do by having the flow vectors as complex numbers. (The 3D problem uses mathematical object like complex numbers, but they provide named unit vectors for all axii/ have 3 parts to them called i,j and k)

A vector operator called curl can be applied to a vector field representation of a flow, to figure out how fast it is rotating...

http://en.wikipedia.org/wiki/Curl_%28mathematics%2...

Hope that helps somewhat. It's not an easy topic.

First, imaginary numbers are actually not "imaginary", they are extra proper observed as "complicated" numbers. actual, they do no longer seem to be that complicated the two. They purely require 2 numbers to quantify the linked fee. as an occasion, an impedance Z = R + j X. the linked fee R is observed as the real component of the impedance, and the section j X is observed as the "imaginary" section. word that an engineer's "j" is = to a mathematician's "i", which represents the sq. root of unfavourable one. complicated numbers are mandatory to outline "vectors" in the X-Y plane that have magnitude and section. EE's signify alerts (sine waves) and impedances using those vectors.