It is used in electrical circuit calculations to describe “negative” electrical flow.

In control system theory. Transfer functions with complex roots have pole-zero plots mapped onto the complex plane along with real roots. Their positions tell characteristics about the system like stability, response time etc, etc…

@ARE_you_kidding_me Most of that is over my head
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A good bit is over mine too

Quantum Field Theory: for example when you are writing Lagrangian for a situation of universe at the very beginning; before anything like Big-Bang or any other occurrence. Some solutions are dealing with complex numbers and indicate vacuum states.

@RedDeerGuy1 – once the complex (real + imaginary) equations are worked out, most control systems work as predicted => math works. That gives you self-driving cars and self-landing rockets. Then normal people just have to type in addresses and press Return for the thing to work. I have worked those equations before in class, but much prefer to have a real EE do it for real products.