What is the use/need of complex numbers in real life if they are imaginary?


What is the use/need of complex numbers in real life if they are imaginary?

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In my mechanical engineering degree we used them in electrical engineering, and in fluid dynamics. They make some calculations a lot easier.
A fuller explanation here, but not suitable for 5 year olds!

They make calculating and understanding things easier. But you don’t need them, it’s possible to reformat maths/physics to not use them.


Sabine’s video on this is a useful insight into the debate on whether imaginary numbers are real or needed.


Complex numbers are often used for audio analysis and quantum physics, because they’re good at describing circular movements and waves.

Also they’re used to calculate rotations in video games and computer graphics. (in this case an even more advanced version called *quaternions* are used, with four total “dimensions” of *real, i, j, k*)

They’re not so much “needed” as “helpful.” A lot of engineering problems, (if I recall from university, particularly electrical and fluid) are greatly simplified when using them.

A lot of useful things in real life are imaginary. Money is just a paper, but it greatly simplifies trade, just one example.

They are just as “imaginary” as negative numbers are. You can’t have negative sheep. If you put three of them in a pen, it’s entirely preposterous to think that you could take five away from there.

Negative numbers just happen to be very useful for representing amounts which can fluctuate between two states. For example, credit and debit. If you deposit five gold pieces to a bank, your balance says “5” which represents the banker owing that much to you. If you go there and withdraw seven gold pieces, the balance says “-2” and represents you owing that much to the bank. At no point do any sort of “anti-gold pieces” actually appear.

Complex numbers are the same. They’re a very useful tool for representing things which don’t flip between two directions, but cycle through four of them. As a tool, it doesn’t really have day-to-day applications to a layperson, but they’re crucial for solving a wide variety of math problems which, for example, let your cellphone process signals.