Imaginary? Really?

At some point we teach students about imaginary numbers.  We define it as the square root of -1.  We show how the pattern repeats every four times it used but are we ever able to provide students with a real situation.  I've been told it is used in electronics but I really have no idea how so I went on the internet to find the answer to this question for the next time I have to teach it.

i is considered an imaginary number,  one used for finding roots of negative numbers, quadratics, etc. 

One reason I didn't realize imaginary numbers appear in electronics is because they use the letter j instead to denote the same thing because i refers to current.  It is primarily found with alternating current which changes from positive to negative sine ways.  Being able to use both real and imaginary numbers help combine alternating currant without being electrocuted.

Imaginary numbers can help describe the movement of shock absorbers in cars as they go over speed bumps, or in modeling how fluids travel around objects in their way, analyzing economic systems and structures using riveted beams, modeling light or water waves, and so many other applications.  Usually, the use of imaginary numbers occurs more frequently in higher level maths.

In addition, you will find imaginary numbers used in signal processing, cellular technology, wireless technology, biology, and radar.  Furthermore, the imaginary number has made an appearance in fictional literature such as The Da Vinci code and The Imaginary by Isaac Asimov where the imaginary number helps describe the behavior of a certain species of squid.

So now when my students ask me about the real life uses of imaginary numbers, I will have an answer.  Let me know what you think, I'd love to hear.  Have a great day.